Locating system and method for determining positions of objects

ABSTRACT

A locating system for determining a position of an object comprises a transmitting station that transmits a first ID signal containing a first identifier of this transmitting station; a receiving station that receives the first ID signal, measures the intensity of the first ID signal, and extracts the first identifier; a data management unit that stores and manages the intensity in association with the first identifier, the intensity and the identifier being supplied from the receiving station; and a positioning computer that estimates the position of the transmitting station using a first correcting formula defining a relation between the intensity and the distance, based on the data stored in the data management unit.

BACKGROUND OF THE INVENTION

[0001] 1. Field of Invention

[0002] The present invention generally relates to a locating system fordetermining the location of a transmitting station attached to an itemor a person, and more particularly to a locating system for efficientlydetermining the positions of a number of transmitting stations indoors,such as in stores, warehouses, and offices, with a high precisionwithout being subjected to much influence from environmental factors.

[0003] 2. Description of the Related Art

[0004] Wireless tags (or transmitting stations) are used in variousfields. For example, a tag system illustrated in FIG. 1 is actuallyworking at many stores. The system shown in FIG. 1 comprises a gate 121and wireless tags 123 attached to items or merchandise. If items 122 aand 122 b having tags 123 a and 123 b, respectively, pass through thegate 121 without paying at a cashier, the system generates alarms. Thissystem is a so-called passive tag system using gates, in which passivetags are used as transmitting stations. The passive tag receives radiowaves generated from the gate 121, modulates the radio waves, andreturns signals to the gate 121. The gate 121 generates alarms whenreceiving the return signals transmitted from the tag 123. The passivetag system in combination with a gate is superior in maintenance becausethe tag (or the transmitting station) 123 does not require a powersource. However, the communication range is limited to several tens ofcentimeters, and therefore it is unsuitable for a long-range tag system.

[0005] On the other hand, a so-called active tag system illustrated inFIG. 2 is known as a long-range tag system. In the active tag system, apower source is provided to each of the transmitting stations 127 a-127f in order to extend the communication range. In general, the active tagsystem uses a frequency band assigned to a specific low power, and iscapable of communicating in the range from several meters to severaltens meters. However, this active radio tag system only has a functionof determining presence or absence of the transmitting stations 127a-127 f (tag 1 through tag 6) in the communication areas 125 a and 125 bof the receiving stations 124 a and 124 b, respectively. If theconventional active tag system (i.e., a combination of activetransmitting stations 127 and receiving stations 124) is used toestimate the position of each transmitting station, the positionestimating accuracy is beyond the communication range (i.e., exceeds thecommunication area size). In order to raise the positioning accuracy,the transmission power of the transmitting station must be lowered, orthe sensitivity of the receiving station must be reduced, whileincreasing the number of receiving stations, to narrow the area coveredby each receiving station.

[0006] To overcome the above-described problems of the active tagsystem, a locating system illustrated in FIG. 3, which is disclosed inJPA (Japanese Patent Laid-open Publication No.) 9-161177, is proposed.The system shown in FIG. 3 includes a transmitting station 131, three ormore base stations 132 a-132 c, and a center station 133 communicatingwith the base stations 132. The transmitting station 131 transmits asignal containing the identification code of the transmitting stationitself and current time (i.e., time of transmission) at a predeterminedtime interval using radio waves. Every time the base stations 132receive the signal from the transmitting station 131, they each transmitthe received signal, together with time of receipt and theiridentification codes, to the center station 133 by radio waves. Thecenter station 133 calculates the distance between the transmittingstation 131 and each of the base stations 132, based on the informationreceived from the base stations 132, and estimates the position of thetransmitting station 131. To be more precise, the center station 133determines the signal propagation time from the time of transmission andtime of receipt and calculates the distance between the transmittingstation 131 and each of the base stations 132 by multiplying thepropagation time with the propagation speed of radio waves. Then, thecenter station 133 estimates the position of the transmitting station131 based on the positional relation with respect to the base stations132.

[0007] The system disclosed in JPA9-161177 can estimate the position ofthe transmitting station by accurately measuring time. However, thesignal transmission interval is generally set long at the transmittingstation 131 in order to keep the life of the battery long. This causes aproblem that precise position information can not be obtained when suchposition information is actually needed. In addition, at least threebase stations 132 must be fixed in order to estimates the position ofthe transmitting station, and if the transmitting station moves out ofthe communication area of the fixed base station, the position of thetransmitting station can not be estimated. Still another problem is thatthere is no information about the environment of the transmittingstation.

[0008]FIG. 4 illustrates another known locating system, which isdisclosed in JAP9-159746. The system shown in FIG. 4 includes atransmitting station 131 that transmits a radio signal, three or morebase stations 132 that receive the radio signal from the transmittingstation 131 and measure the intensity of the received signal, and acenter station 133 that estimates the position of the transmittingstation 131 based on the intensity of the received signal supplied fromeach base station 132. In this system, the transmitting station 131generates and transmits radio signals during the positioning operation.Each of the base stations 132 supplies the measuring result of thesignal intensity to the center station 133. The center station 133calculates the distance between the transmitting station 131 and each ofthe base stations 132 from the intensity, and estimates the position ofthe transmitting station 131 based on the positional relation betweenthe transmitting station 131 and each of the base stations 132.

[0009] A table listing the relations between intensities of the receivedsignals and the corresponding distances is stored in the center station133 in advance. The center station 133 determines the distance byapplying the received intensity to the table. This system is capable ofestimating the position of the transmitting station 131 by creating anaccurate table indicating the relation between the intensity and thedistance. However, in order to specify the position, at least three basestations must be fixed. If the transmitting station 131 moves away fromthe communication area of the base station, the position of thetransmitting station 131 can not be estimated any longer.

[0010] Thus, the conventional “passive tag system” is unsuitable for along-range radio tag system because its communication range is as shortas several ten centimeters.

[0011] The conventional “active tag system” requires the number ofreceiving stations to be increased in order to improve the positioningaccuracy.

[0012] The conventional locating system illustrated in FIG. 3, whichestimates the distance based on the transmission time, needs to set thesignal transmission interval long in order to keep the life of thebattery of the transmitting station long. For this reason, it isdifficult for this system to obtain accurate position information whenit is actually required. In addition, at least three base stations haveto be fixed to estimate the position, and if the transmitting stationmoves out of the communication area, the position of the transmittingstation can not be estimated any longer. This system can not determineunder what environment the transmitting station is operating.

[0013] The conventional locating system illustrated in FIG. 4, whichdetermines the distance based on the intensity of the received signal,requires at least three base stations to be fixed. If the transmittingstation is out of the communication area of the base station, theposition can not be estimated any longer.

[0014] Although a positioning means making use of a GPS may be effectiveoutdoors, it is unsuitable indoors because of reflected waves. Using anabsolute time difference, as in a GPS, under the influence of reflectedwaves is ineffective because the error becomes too large. Even ifestimating a position using amplitude information, the relation betweenthe distance and the intensity of the received signal does not agreewith the Friis' formula in many cases.

[0015] As is well known, Friis' formula is expressed by $\begin{matrix}{L = {20 \times {\log_{10}( \frac{4\pi \quad d}{\lambda} )}}} & (0)\end{matrix}$

[0016] where L denotes the propagation loss, d denotes the distance, andλ denotes the wavelength.

[0017] The reason why Friis' formula does not work for indoorspropagation is that the receiving station is located in hiding, or localfluctuation occurs in intensity of the received signal due to influenceof reflected waves.

SUMMARY OF THE INVENTION

[0018] The present invention was conceived in view of theabove-described problems in the prior art, and it is an object of theinvention to overcome the limited communication range, which is theproblem in the conventional passive tag system, and avoid undesirableincrease in the number of receiving stations when estimating a positionaccurately, which is the problem in the conventional active tag system.

[0019] It is another object of the invention to estimate the position ofa transmitting station with high precision even indoors by taking intoconsideration the environment surrounding the transmitting station.

[0020] It is still another object of the invention to allow a user toobtain accurate position information when such position information isactually required.

[0021] It is yet another object of the invention to eliminate thenecessity of fixing three or more base stations (or receiving stations)when estimating a position of a transmitting station.

[0022] It is yet another object of the invention to continuouslyestimate the position of a transmitting station even if the transmittingstation moves out of the communication area of a fixed base station.

[0023] These objects are realized in a locating system and methodprovided according to the invention. Such a system and method areapplicable not only to monitoring dangerous objects or preventing theft,but also to controlling the inventory and managing the assets inwarehouses or offices in an efficient manner.

[0024] To achieve the above-described objects, in one aspect of theinvention, a system for determining a position of an object comprises(a) a transmitting station configured to transmit a first ID signalcontaining a first identifier in a periodic manner, (b) a receivingstation configured to receive the first ID signal, measure the intensityof the first ID signal, and read the first identifier, (c) a datamanagement unit configured to store and manage the intensity inassociation with the first identifier that are supplied from thereceiving station, and (d) a positioning computer configured to estimatethe position of the transmitting station using the data managed by thedata management unit.

[0025] The positioning computer determines a first correcting formuladefining intensity “e” of a received signal as a function of distance“d”. The positioning computer then estimates the position of thetransmitting station using the first correcting formula and known (oravailable) position information.

[0026] If the position of the i^(th) transmitting station is (xi, yi)and the j^(th) receiving station is (uj, vj), the distance d_(ij)between the i^(th) transmitting station and the j^(th) receiving stationis

d _(ij)={square root}{square root over ((x ₁ −u _(j))²+(y _(i) −v_(j))²)}  (1)

[0027] The first correcting formula is expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂  (2)′

[0028] or

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)  (24)′

[0029] where e_(ij) is the intensity of the ID signal transmitted by thei^(th) transmitting station and received at the j^(th) receivingstation, and S1 and S2 are correcting coefficients.

[0030] Preferably, the first formula further includes at least one of anenvironmental coefficient Kti of the transmitting station or anenvironmental coefficient Krj of the receiving station. This arrangementallows more accurate position estimation taking the surroundingenvironment into account.

[0031] The receiving station may have an activation signal generatorthat generates an activation signal for causing the transmitting stationto transmit another ID signal. In this case, the receiving stationtransmits the activation signal to the transmitting station, and thetransmitting station transmits a second ID signal containing a secondidentifier upon receiving the activation signal.

[0032] The transmitting station has a sensor for sensing changes causedby external factors. When detecting any changes, the transmittingstation transmits a third ID signal containing a third identifier to thereceiving station. Such changes include vibration or acceleration due toexternally applied force, and a change in incident light, temperature,humidity and other parameters.

[0033] By using the activation signal and/or the sensor, necessaryposition information can be obtained, taking environmental changes intoaccount, when such position information is actually required (forexample, when the receiving station is looking for the transmittingstation or when the transmitting station has physically moved to adifferent place) In addition, the life of the battery is extendedbecause it is unnecessary to shorten the transmission interval ofperiodic signals.

[0034] The receiving station also has a time computation unit thatmeasure a transmission time required to acquire the second ID signal inresponse to the activation signal. In this case, the positioningcomputer determines a second correcting formula that defines a relationbetween a signal propagation time through the air and a distance. Thepositioning computer then estimates the position of an unknowntransmitting station using the second correcting formula and known (oravailable) position information.

[0035] The second correcting formula is expressed as

p _(ij) =f ₁(t _(ij) ,e _(ij))=t _(ij) −B−g exp(−h×e _(ij))=Kd _(ij)=K{square root}{square root over ((u _(i) −u _(j))²+(v ₁ −v_(j))²)}  (9)′

[0036] where p_(ij) is propagation time taken for the ID signal topropagate through the air from the i^(th) transmitting station locatedat (ui, vi) to the j^(th) receiving station located at (uj, vj), e_(ij)is the intensity of the ID signal received at the j^(th) receivingstation, t_(ij) is transmission time required for the j^(th) receivingstation to acquire the ID signal in response to the activation signal,d_(ij) is the distance between the i^(th) transmitting station and thej^(th) receiving station, B, g, and h are correcting coefficients, and Kis a proportional constant.

[0037] With the second correcting formula, the propagation rate of asignal carried by electromagnetic waves or ultrasonic waves isdetermined based on the actually measured values (e_(ij) and t_(ij)),using an approximate function. Consequently, it is not necessary toadditionally measure the temperature and the humidity of the air for thecorrection. In addition, since the relation between the propagation timeand the distance is corrected based on the actually measured values, theestimation accuracy is improved even if high-speed operation can not becarried out due to aiming to achieve low power consumption.

[0038] The positioning system may include a single fixed-positionreceiving station (i.e., a first receiving station) and a single movingreceiving station (i.e., a second receiving station) in order to reducethe number of the fixed-position receiving stations that function asbase stations. This arrangement also allows the system to correctlyestimate the position of a transmitting station that has moved away fromthe communication area of the fixed-position receiving station. In thiscase, the positioning computer determines at least one of the first andsecond correcting formulas using position information about a knowntransmitting station supplied from the fixed (or the first) receivingstation. Then, (A) the positioning computer estimates the position ofthe moving (or the second) receiving station using the correctingformula, as well as signal information transmitted from a known orposition-estimated transmitting station and received at the movingreceiving station and the position information about the known orposition-estimated transmitting station. Furthermore, (B) thepositioning computer estimates the position of a transmitting stationwhose position is unknown (hereinafter, simply referred to as an“unknown transmitting station”) using signal information transmittedfrom the unknown transmitting station and received at the fixed-positionreceiving station or the moving receiving station at an estimatedposition, as well as position information about the fixed-positionreceiving station or the estimated position of the moving receivingstation. The positioning computer repeats processes (A) and (B) tosuccessively acquire position information of unknown transmittingstations as the moving receiving station travels.

[0039] Another effective structure for reducing the number of receivingstations is employing a single moving station, without using afixed-position receiving station. In this case, the positioning computerdetermines at least one of the first and second correcting formulasusing position information about transmitting stations whose positionsare known, which are supplied from the moving receiving station whoseposition is unknown. Then, (A) the positioning computer estimates thecurrent position of the receiving station using signal informationtransmitted from known or position-estimated transmitting stations tothe receiving station, position information about the known orposition-estimated transmitting stations, and the determined correctingformula(s). Then, (B) the positioning computer estimates the position ofan unknown transmitting station using signal information supplied fromthe unknown transmitting station to the receiving station located at thecurrent position, and position information about the current position ofthe receiving station. The positioning computer repeats processes (A)and (B) to successively acquire position information of unknowntransmitting stations as the moving receiving station travels.

[0040] By using a moving receiving station solely or in combination witha fixed-position receiving station, the presence and the positions ofmultiple transmitting stations can be determined and controlledaccurately over a wide area.

[0041] As a carrier of the signals transmitted between the transmittingstation and the receiving station, electromagnetic waves including radiowaves and infrared rays, or sound waves including ultrasonic waves andaudible waves can be used. In the specification and claims, the term“sound wave” includes both ultrasonic wave and audible wave. Thecarriers for the activation signal and the ID signal may be the same asor different from each other.

[0042] In the second aspect of the invention, a locating method fordetermining a position of an object is provided. The method comprisesthe steps of receiving at a receiving station a first ID signalcontaining a first identifier of a transmitting station; measuring theintensity of the first ID signal; determining a first correcting formulathat defines a relation between intensity and distance; and estimating aposition of an unknown transmitting station using the first correctingformula.

[0043] Distance d_(ij) from the i^(th) transmitting station located at(xi, yi) to the j^(th) receiving station located at (uj vj) is

d _(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j) ²)}  (1)

[0044] and the first correcting formula is expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂  (2)′

[0045] where e_(ij) is the measured intensity, and S1 and S2 arecorrecting coefficients.

[0046] Preferably, the first correcting formula includes at least one ofan environmental coefficient Krj for the receiving station and anenvironmental coefficient Kti for the transmitting station. If theenvironmental coefficient Krj for the receiving station is used, thefirst correcting formula is expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)″

[0047] In this case, unknown parameters S1, S2, and Krj are determinedbased on known position information, and the position of the i^(th)transmitting station is estimated using the determined values of thecoefficients.

[0048] If the environmental coefficient Kti for transmitting station isused, the first correcting formula is expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂ −K _(ti)  (2)″′

[0049] In this case, unknown parameters S1, S2 and Kti are determinedbased on known position information, and the position of the i^(th)transmitting station is estimated using the determined values of thecoefficients.

[0050] A modified first correcting formula may be used. The modifiedfirst correcting formula is expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)  (24)′

[0051] Preferably, the modified first correcting formula also includesat least one of an environmental coefficient Krj for receiving stationand an environmental coefficient Kti for transmitting station, inaddition to the correcting coefficients S1 and s2. If using Kri, themodified first correcting formula is expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)−K _(rj)  (24)

[0052] If using Kti, the modified first correcting formula is expressedas

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)−K _(ti)  ( 24 )″

[0053] The locating method further comprises the steps of transmittingan activation signal from the receiving station to the transmittingstation; receiving at the receiving station a second ID signalcontaining a second identifier transmitted in response to the activationsignal; and measuring a transmission time “t” required to acquire thesecond ID signal in response to the activation signal. In this case, theposition of an unknown transmitting station is estimated using a secondcorrecting formula that defines a relation between a propagation time“p” of the signal through the air and a distance.

[0054] The second correcting formula is expressed as

p _(ij) =f ₁(t _(ij) ,e _(ij))=Kd _(ij) =K{square root}{square root over((x _(i) −u _(j))²+(y _(i) −v _(j))²)}  (9)″

[0055] where d_(ij) is a distance from the i^(th) transmitting stationlocated at (xi, yi) to the j^(th) receiving station located at (uj, vj)p_(ij) is a signal propagation time through the air, t_(ij) is atransmission time required to acquire the second ID signal, and K is aproportional constant.

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Other objects, features, and advantages of the invention willbecome more apparent from the following detailed description when readin conjunction with the accompanying drawings, in which

[0057]FIG. 1 illustrates a conventional passive tag system using a gate;

[0058]FIG. 2 illustrates a conventional active tag system;

[0059]FIG. 3 illustrates a conventional locating system using timeinformation;

[0060]FIG. 4 illustrates a conventional locating system using theintensities of received signals;

[0061]FIG. 5 illustrates a locating system according to the firstembodiment of the invention;

[0062]FIG. 6 illustrates the structures of the transmitting station andthe receiving stations used in the locating system of the firstembodiment;

[0063]FIG. 7 illustrates an example of the motion sensor used in thetransmitting station shown in FIG. 6;

[0064]FIG. 8 illustrates operation flows of the locating systemaccording to the first embodiment;

[0065]FIG. 9 illustrates the measuring result of the positions oftransmitting stations using the locating system according to the firstembodiment;

[0066]FIG. 10 illustrates a locating system according to the secondembodiment of the invention;

[0067]FIG. 11 illustrates the structures of the transmitting station andthe receiving station used in the locating system of the secondembodiment;

[0068]FIG. 12 illustrates the operation flow of the transmitting stationaccording to the second embodiment;

[0069]FIG. 13 illustrates the operation flow of the receiving stationaccording to the second embodiment;

[0070]FIG. 14 illustrates the operation flow of the positioning computeraccording to the second embodiment;

[0071]FIG. 15 illustrates a first modification of the locating system ofthe second embodiment;

[0072]FIG. 16 illustrates the structures of the transmitting station andthe receiving station used in the first modification shown in FIG. 15;

[0073]FIG. 17 illustrates a second modification of the locating systemof the second embodiment;

[0074]FIG. 18 illustrates the structures of the transmitting station andthe receiving station used in the second modification shown in FIG. 17;

[0075]FIG. 19 illustrates the operation flow of the positioning computerused in the second modification;

[0076]FIG. 20 illustrates a third modification of the locating system ofthe second embodiment;

[0077]FIG. 21 illustrates the structures of the transmitting station andthe receiving station used in the third modification shown in FIG. 20;

[0078]FIG. 22 illustrates a locating system according to the thirdembodiment of the invention;

[0079]FIG. 23 illustrates the structures of the transmitting station andthe receiving station used in the locating system of the thirdembodiment;

[0080]FIG. 24 illustrates the operation flow of the receiving stationused in the third embodiment;

[0081]FIG. 25 illustrates the operation flow of the positioning computerused in the third embodiment;

[0082]FIG. 26 illustrates a locating system according to the fourthembodiment of the invention;

[0083]FIG. 27 illustrates the structures of the transmitting station andthe receiving station used in the locating system of the fourthembodiment;

[0084]FIG. 28 illustrates the operation flow of the receiving stationused in the fourth embodiment;

[0085]FIG. 29 illustrates the operation flow of the positioning computerused in the fourth embodiment;

[0086]FIG. 30 illustrates a locating system according to the fifthembodiment of the invention;

[0087]FIG. 31 illustrates the structures of the transmitting station andthe receiving station used in the locating system of the fifthembodiment;

[0088]FIG. 32 illustrates the operation flow of the positioning computerused in the fifth embodiment;

[0089]FIG. 33 illustrates a measuring result of the position of atransmitting station using the modified first correcting formulaaccording to the sixth embodiment of the invention; and

[0090]FIG. 34 illustrates another measuring result of the position of adifferent transmitting station using the modified first correctingformula according to the sixth embodiment of the invention.

DATAILED DESCRIPTION OF THE EMBODIMENTS

[0091] The present invention will now be described in detail withreference to the attached drawings.

[0092] [First Embodiment]

[0093]FIG. 5 schematically illustrates an example of the locating system1 according to the first embodiment of the invention, and FIG. 6illustrates the transmitting station 21 and the receiving station 31used in the locating system 1. The locating system 1 includestransmitting stations 21 (T1-T8), receiving stations 31 (R1-R4), aserver 12 connected to the receiving stations 31 and functioning as adata management unit, and a positioning computer 11 connected to theserver 12. The locating system 1 also includes user terminals 3 a-3 cconnected to the positioning computer 11. These components are connectedto one another via LAN 2.

[0094] In the example shown in FIG. 5, the receiving stations 31 (R1-R4)are fixed, and their positions are known. The transmitting stationsT1-T4 are attached to the receiving stations R1-R4, respectively, andtherefore, the positions of the transmitting stations T1-T4 can beregarded the same as those of the receiving stations R1-R4. Thepositions of the transmitting stations T5-T8 are unknown. The positionof the j^(th) receiving station, which is known in advance, is (uj, vj),and unknown position of the i^(th) transmitting station is expressed as(xi, yi). Each transmitting station 21 transmits a unique signal, andthe receiving stations 31 receive the signals from the transmittingstations 21. The intensity of the signal transmitted by the i^(th)transmitting station and received at the j^(th) receiving station isexpressed as e_(ij). The distance between the i^(th) transmittingstation and the j^(th) receiving station is expressed as d_(ij). Forexample, the distance from transmitting station T5 positioned at (x5,y5) to receiving station R1 is d51, and the intensity of the signaltransmitted by T5 and received at R1 is e51.

[0095] The transmitting station 21 has a microcontroller 22, atransmitter 23, an ID signal generator 25, and a motion sensor 13. TheID signal generator 25 periodically generates an ID signal containing aunique identifier (ID) of that transmitting station 21. The ID signalgenerator also generates an ID signal containing the identifier when themotion sensor 13 senses any motion of the transmitting station.

[0096] An example of motion sensor 13 is illustrated in FIG. 7. In thisexample, the motion sensor 13 includes an acceleration sensor using aninverted pendulum 14, and a hold circuit 15 is connected to the motionsensor 13. The hold circuit 15 is also connected to the oscillator 16 ofthe transmitting station 21, and it turns on the battery 17 of theoscillator 16 for a few minutes only when the electrodes 14 a and 14 bof the motion sensor 13 come into contact with each other (oralternatively, when they separate from each other).

[0097] The hold circuit 15 has a function of setting a long oscillationperiod, regardless of the ON/OFF operation of the motion sensor(acceleration sensor) 13. This function is effective for constantlycontrolling the position of the transmitting station 21. The oscillationperiod does not have to be perfectly constant. By randomly varying theoscillation period by several percentages over period, signal beingsimultaneously transmitted from different stations can be avoided. Themotion sensor 13 allows the transmitting station 21 to set theoscillation period long because the periodic ID signal does not have tobe transmitted frequently when the transmitting station 21 isstationary. This arrangement can reduce power consumption and extend thelife of the battery. In addition, the log file can be made smaller.

[0098] All of the transmitting stations T1-T8 may employ the samestructure as shown in FIG. 6, or alternatively, two different types oftransmitting stations may be used. In the latter case, the motion sensor13 is provided to the transmitting stations T5-T8 whose positions areunknown, while the fixed transmitting stations T1-T4 simply have ashort-period oscillating function without the motion sensor 13.

[0099] Returning to FIG. 6, the receiving station 31 has amicrocontroller 32, a receiver 33, and an anti-collision determinationunit 36. The receiver 33 receives signals, and measures the intensitiesof the received signals. The receiver 33 then supplies the receivedsignals to the anti-collision determination unit 36 which reads (orextracts) the identifiers from the received signals. The receivingstation 31 supplies the intensities of the received signals and thecorresponding identifiers, together with time stamps to the server 12.The server 12 records and stores each of the intensities in associationwith the corresponding identifier and time stamp. Time stamps may becreated by the server 12 when the server 12 receives signal informationfrom the receiving station 31.

[0100] The positioning computer 11 estimates the position oftransmitting station T5 (in example shown in FIG. 5) using informationabout this transmitting station stored in the server 12. The estimationresult is also stored in the server 12. The user can obtain the positionof the transmitting station T5 by inputting the identifier of thistransmitting station through the user terminal 3 to be retrieved in theserver 12.

[0101] The positioning computer 11 determines a first correcting formuladefining a relation between intensity and distance in order toaccurately estimate the position of either a transmitting station or areceiving station under the indoors environment. As has been describedabove, the intensity e_(ij) of a received signal is actually measured ata receiving station under the indoors propagation condition. Thepositioning computer 11 determines the relation between the intensitye_(ij) and the distance d_(ij) from the transmitting station 21 to thereceiving station 31 using the actually measured values. The firstcorrecting formula is a corrected Friis' formula using correctingcoefficients including environmental coefficients. Since the distance,and therefore, the positional coordinates of a transmitting station areestimated based on the actually measured value taking the correctingfactors into account, the positioning accuracy is improved even indoors.

[0102] The algorithm using a corrected Friis' formula (that is, thefirst correcting formula) will be explained in detail below. For thesake of simplicity, explanation will be made using two-dimensionalcoordinates below; however, the positioning computer 11 estimatespositions using three-dimensional (special) coordinates in actual use.

[0103] <Algorithm of Corrected Friis' Formula>

[0104] If a known position of the j^(th) receiving station is (uj,vj)and if a position of the i^(th) transmitting station is (xi,yi), thenthe distance between the i^(th) transmitting station and the j^(th)receiving station is expressed by Equation (1).

d _(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j))²)}  (1)

[0105] Then, environmental coefficient Krj for the j^(th) receivingstation is defined. Environmental coefficient Krj is an index indicatinghow the sensitivity of the receiving station changes from the idealcondition. Similarly, environmental coefficient Kti for the i^(th)transmitting station is defined.

[0106] First, the Friis' formula is corrected using correctingcoefficients S1, S2, and an environmental coefficient Krj to define arelation between distance “d” and intensity “e”, on the assumption thatdistance and intensity are in the logarithmic relation. The correctedformula is expressed as

e _(ij) =S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)

[0107] This corrected formula is referred to as a first correctingformula.

[0108] The coefficients S1, S2, and Krj are determined using knowninformation. In the example shown in FIG. 5, these coefficients (i.e.,unknown parameters) are determined using the measured intensities e_(ij)of the signals received from transmitting stations T1-T4 whose positionsare known (because they are attached to the fixed-position receivingstations R1-R4). The corresponding distances d_(ij) are also known. Thesolutions for these unknown parameters that minimize the error can beobtained by minimizing estimation function “q” given by Equation (3).$\begin{matrix}{q = {\sum\limits_{j = 1}^{rn}{\sum\limits_{i = 1}^{tn}( {e_{ij} - {{\overset{\Cap}{S}}_{1}{\log_{10}( d_{ij} )}} - {\overset{\Cap}{S}}_{2} + {\overset{\Cap}{K}}_{rj}} )^{2}}}} & (3)\end{matrix}$

[0109] where rn denotes the number of receiving stations at knownpositions, and tn denotes the number of transmitting stations at knownpositions. In the example of FIG. 5, both rn and tn are four (4), andsixteen (16=4×4) simultaneous equations stand. Consequently, sixunknowns (S1, S2, Kr1-Kr4) are all solved. To clarify the explanation,the unknowns are marked with an arc above the symbols in Equation (3).

[0110] There are many methods for solving Equation (3). Althoughdetailed explanation for these methods will not be made, for example,partially differentiating function q with respect to each variable, andthe numerical solutions that make the respective partial differentialszero can be obtained by, for example, the Newton method. Alternatively,the simplex method, the steepest descent method (or saddle pointmethod), methods using neural networks can be used. Using any one ofthese methods, the correcting coefficients S1 and S2 and theenvironmental coefficient Krj can be determined.

[0111] If the number of transmitting stations or receiving stations atknown positions is insufficient and adequate equations do notsimultaneously stand, then only the correcting coefficients S1 and S2are used in the first correcting formula without using environmentalcoefficient Krj. Even without the environmental coefficient, asatisfactory correcting effect can be achieved.

[0112] Next, environmental coefficient Kti for a target transmittingstation whose position is unknown (simply referred to as “unknowntransmitting station”) will be introduced. Although the transmittingintensity at a transmitting station is constant, the environmentalcoefficient varies depending on the location, and therefore, theintensity of the received signal varies. Accordingly, an environmentalcoefficient for transmitting station is introduced. For example, theintensity of a signal received at a known receiving station (e.g., R1)from an unknown transmitting station (e.g, T5) is expressed usingenvironmental coefficient Kt5, in addition to the correctingcoefficients S1 and s2, and environmental coefficient Kr1. Byintroducing the environmental coefficient Kti for a transmittingstation, a distance md_(ij) derived from the measured intensity isexpressed as Equation (4). $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj} + K_{ti}})}/S_{1}}} & (4)\end{matrix}$

[0113] Now, the position and the environmental coefficient Kti of thetarget (unknown) transmitting station “i” are determined by minimizingestimation function hi expressed as Equation (5). $\begin{matrix}{h_{i} = {\sum\limits_{j = 1}^{rn}( {10^{{({e_{ij} - S_{2} + K_{rj} + {\overset{\Cap}{K}}_{ti}})}/S_{1}} - \sqrt{( {{\hat{x}}_{i} - u_{j}} )^{2} + ( {{\overset{\Cap}{y}}_{i} - v_{j}} )^{2}}} )^{2}}} & (5)\end{matrix}$

[0114] The unknowns in Equation (5) are marked with an arc above thesymbols for clarification. Using the above-described method, theposition of an unknown transmitting station can be estimated accuratelyeven if the number of fixed-position receiving station is not so large.

[0115] The estimated position of the transmitting station is stored inthe server 12. As has been explained, in order to check the position ofa target transmitting station, the user (or the manager) simply inquiresof the server 12 via LAN 2 by inputting the identifier of the targettransmitting station through the user terminal 3.

[0116] Next, a situation in which a transmitting station is located atan obstructed place will be considered. Even through a transmittingstation is located within a communicable area of a receiving stationfrom a viewpoint of loss in free space, the signal transmitted from thattransmitting station may not be received at the receiving station whenthe transmitting station is obstructed with respect to that receivingstation. In this case, it may appear that the receiving station does nothave information about that transmitting station.

[0117] However, not receiving a signal from a specific transmittingstation means that this specific transmitting station is located at adisadvantageous (or farther) position as compared with thosetransmitting stations whose signals are received. Accordingly, the factthat a signal from a specific transmitting station can not be receivedis worth while as information for position estimation. Therefore, thelocating system according to the invention makes use of such obstructedinformation as a restrictive condition.

[0118] For example, a signal from transmitting station T2 is received atreceiving stations R1, R2, and R3, but is not received at R4. In thiscase, restrictive conditions

[0119] d21<d24

[0120] d22<d24

[0121] d23<d24

[0122] are added. Thus, even unknown information is not discarded, andinstead, it is effectively used in position estimation.

[0123] The positioning computer 11 repeatedly estimates and updatespositions of transmitting stations using update information. As has beendescribed above, each transmitting station 21 has a motion sensor 13,and transmits' an ID signal when it physically moves. With thisarrangement, the current position of a transmitting station is estimatedand stored in the server 12 even if the interval of periodic signals islong.

[0124]FIG. 8 illustrates an example of operation flows of the locatingsystem according to the first embodiment of the invention. Each of thetransmitting stations T1-T4 fixed to the receiving stations R1-R4transmits a periodic ID signal at a predetermined time interval (S101and S102). On the other hand, in each of the unfixed transmittingstations T5-T8, the microcontroller 22 monitors the motion sensor 13 todetermine whether or not acceleration has been applied to thetransmitting station (S103). If acceleration has been applied (YES inS103) and a predetermined time has passed (YES in S101), thetransmitting station transmits an ID signal containing a uniqueidentifier.

[0125] The receiving station 31 receives ID signals from the respectivetransmitting stations and measures the intensities of the received IDsignals (S111). Then, the receiving station 31 supplies the measuredintensities and corresponding time stamps to the server 12 (S112). Theidentifiers of the transmitting stations read from the ID signals andthe identifier of the receiving station itself are also supplied to theserver 12. Time stamps may be created at the server 12 when receivingthe information from the receiving station 31.

[0126] The positioning computer 11 checks time stamps in data stored inthe server 12 and compares the current data with the previous data(S131) to determine if the current data has been updated (S132). Ifthere are data updated from the previous ones (YES in S132), data offixed-position transmitting stations (T1-T4 in example shown in FIG. 5),the positions of which are known in advance, are extracted from all theupdated data (S133). Then, coefficients S1, S2 and environmentalcoefficient Krj are determined so as to minimize Equation (3) and thefirst correcting (propagation) formula is determined (S134). Then,Equation (5) is solved with respect to all the data about unfixedtransmitting stations (T5-T8) to estimate the positions of thesetransmitting stations, and the estimation results are stored in theserver 12, together with the environmental coefficient Kti of thetransmitting stations (S135). The estimated positions are compared withthe previous results to select those transmitting stations whosepositions have been changes a predetermined value or more (YES in S136)and those transmitting stations whose signals were not received at anyof the receiving stations (YES in S137). The data of the selectedtransmitting stations are recorded in the server 12 (S138), and an alertmessage is supplied to the associated user terminal (S139).

[0127] An example of a data structure for recording signal informationsupplied from the receiving stations in the server 12 is shown in Table1, and an example of a data structure for recording the estimationresults supplied from the positioning computer 11 in the server 12 isshown in Table 2. In Tables, “RS ID” stands for receiving stationidentifier, and “TS ID” stands for transmitting station identifier.TABLE 1 DATA STRUCTURE OF SIGNAL INFORMATION SUPPLIED FROM RECEIVINGSTATION RS ID TS ID TIME STAMP INTENSITY 0001 0015 16:3:20 24

[0128] TABLE 2 DATA STRUCTURE OF ESTIMATION RESULTS SUPPLIED FROMPOSITIONING COMPUTER TS ID TIME STAMP ESTIMATION (X, Y) ENV'L COEFF.0015 17:22:21 11.95, 9.25 32.4

[0129] Environmental coefficient Kti reflects the environmentsurrounding a transmitting station, and it provides useful informationwhen actually trying to determine the location of the transmittingstation. If the environmental coefficient is large, it indicates thatthe transmitting station is located at an obstructed place with respectto the receiving station. If the environmental coefficient is small, thetransmitting station is located at an open space or an unobstructedplace. Adding such environmental information to the estimated positionallows the user to actually find the target transmitting station.

[0130] The user terminal 3 has a function of receiving an alert messagesupplied from the positioning computer 11, as well as a function ofretrieving the position of a target transmitting station. The userinputs the identifier (ID) of the target transmitting station into theuser terminal (S121). The user terminal accesses the server 12 throughLAN 2 (in the example shown in FIG. 5), or alternatively via radio wave(S122). The past record about the target transmitting station isretrieved in the server 12, and the corresponding time stamp, positioninformation, environmental coefficient of the transmitting station aredisplayed on the user terminal (S123). The user can obtain the positionof the transmitting station at a time described by the time stamp, andcan estimate whether the transmitting station is located at an openspace from the value of the environmental coefficient Kti. Furthermore,by checking the record over a certain period of time, the user candetermine when acceleration was applied (which means when thetransmitting station moved).

[0131] As has been described above, the locating system according to thefirst embodiment uses the first correcting formula, and accuratelyestimates the positions of multiple transmitting stations simultaneouslyusing actually measured signal intensities and known positioninformation.

[0132]FIG. 9 illustrates the position estimation result using thelocating system 1 of the first embodiment. Receiving stations are fixedat positions P1-P6. The positions of transmitting stations (1 through16) are estimated using the information supplied from these receivingstations. The actual positions of the transmitting stations are markedwith *, and the estimated positions are marked with white rectangles.The lines connecting the actual positions to the corresponding estimatedpositions represent the signal propagation condition. The dashed lineindicates a good condition, and the bold line indicates a bad condition.The square in the graph is a unit area on the floor, and a side is 1.35m.

[0133] From this estimation result, the minimum error was only 13.5 cm,and the maximum error is about 4.5 m. The root-mean-square error is 2.3m, and the error for the transmitting stations 1, 2 and 12, which arelocated under a relatively good propagation condition, is within 1 m. Bycarrying out the operation flow of the positioning computer 11 shown inFIG. 8 using the first correcting formula, the positions of multipletransmitting stations can be estimated at high accuracy taking theenvironmental factors into account.

[0134] Although the explanation has been made using an example of atransmitting station or a tag as the object (or the target) of positionestimation, the target is not limited to a transmitting station. Forexample, equipment having both the transmitting function and thereceiving function, such as cellular phones or mobile terminals, may beused as the target. In this case, the transmitting function of suchequipment is utilized for specifying the position of a person who holdsthe equipment.

[0135] [Second Embodiment]

[0136]FIG. 10 illustrates a schematic diagram of the locating systemaccording to the second embodiment of the invention, and FIG. 11illustrates the transmitting station 21 and the receiving station 31used in the second embodiment. In the second embodiment, the receivingstation periodically transmits an activation signal to the transmittingstation. The transmitting station transmits an ID signal, which isdifferent from the spontaneously generated ID signal, upon receiving theactivation signal. Accordingly, the transmitting station generates threedifferent kinds of ID signals, that is, (1) a periodic signal (i.e., thefirst ID signal) spontaneously generated by, for example, a built-inoscillator, (2) a signal (i.e., the second ID signal) generated inresponse to the activation signal, and (3) a signal (i.e., the third IDsignal) generated when detecting a change due to external factors.

[0137] In the example shown in FIG. 10, both the activation signal andthe ID signal are transmitted via electromagnetic waves. Theconfiguration of the system, in which the receiving stations R1-R4, theserver 12, the positioning computer 11, and the user terminals 3 a-3 care mutually connected via LAN 2, and the operation of the user terminalare the same as those in the first embodiment, and explanation for themwill be omitted.

[0138] The transmitting station 21 has a microcontroller 22, atransmitter 23, an ID signal generator 25, and a sensor 26. The IDsignal generator 25 periodically generates an ID signal containing aunique identifier (ID) of that transmitting station 21. Themicrocontroller 22 controls the operation of the transmitting station21, and has built-in memories, such as ROM and RAM. The receiver 24receives the activation signal transmitted from the receiving stationand supplies the activation signal to the ID signal generator 25. Thesensor 26 detects changes in various parameters, which are caused byexternal factors 27, and supplies the detection result to the ID signalgenerator 25. The ID signal generator 25 generates the above-describedthree kinds of ID signals (1) in a periodic manner at a relatively longinterval, (2) when receiving the activation signal from the receivingstation, and (3) when detecting a change. In this regard, the changedetected by the sensor 26 may function as an activation signal to causethe ID signal generator to produce an identifier; however, it must bedistinguished from the activation signal generated and transmitted bythe receiving station.

[0139] The sensor 26 detects not only acceleration (or a change inmotion), but also environmental changes, such as a change in incidentlight, temperature, humidity, and other factors. For example, when atransmitting station (or a tag attached to an item) moves from a darkplace (such as a stack room) to a bright place, the sensor 26 operatesand causes the transmitting station to transmit an ID signal. This IDsignal is received at the receiving stations, and the intensitiesmeasured at the respective receiving stations are supplied to the server12. Consequently, the positioning computer 11 estimates the new positionof the transmitting station that has moved to the bright place toupdates the position information. Another example is when a transmittingstation moves from an air-conditioned place to a non-conditioned place,the sensor 26 detects a change in temperature and humidity and causesthe transmitting station to transmit an ID signal. The sensor 26 isrealized by a combination of a light sensor, a temperature sensor, ahumidity sensor, a motion sensor, and other types of sensors.

[0140] Preferably, the transmitting station 21 has a function of settinga long oscillation period, regardless of the ON/OFF operation of thesensor 26 for the purpose of effective control of the position of thetransmitting station 21. The oscillation period does not have to beperfectly constant. By randomly varying the oscillation period with awidth of several percents of the period, signal being transmittedsimultaneously from different stations can be avoided.

[0141] The receiving station 31 has a microcontroller 32, a receiver 33,a transmitter 34, an activation signal generator 35, and ananti-collision determination unit 36. The microcontroller 32 controlsthe operation of the receiving station 31 and has built-in memories,such as ROM and RAM. The activation signal generator 35 generates anactivation signal in a periodic manner. The receiver 33 receives firstthrough third ID signals and measures the intensities of the respectivesignals. The anti-collision determination unit 36 reads the identifiers(first, second, and third identifiers) from the respective types of IDsignals. The receiving station 31 then supplies the intensities of thereceived signals and the corresponding identifiers, together with timestamps to the server 12. The server 12 records and stores each of theintensities in association with the corresponding identifier and timestamp. Time stamps may be created by the server 12 when the server 12receives the signal information from the receiving station 31.

[0142]FIG. 12 illustrates the operation flow of the transmitting station21 according to the second embodiment of the invention. The transmittingstation 21 generates and transmits different kinds of ID signals withdifferent identifiers depending on the situations.

[0143] (A) When receiving an activation signal from the receivingstation (YES in S201), it is confirmed whether the activation signal isan expected prescribed activation signal (S201). If it is the expectedactivation signal (YES in S201) the ID signal generator 25 generates atype-a ID signal containing an identifier of type a, which istransmitted to the receiving station (S203).

[0144] (B) The transmitting station also transmits a type-b ID signal ina periodic manner every predetermined time interval (S204 and S205).

[0145] (C) In addition, when the sensor 26 detects a change due toexternal factors (YES in S206), it is confirmed if a predeterminedamount of time has passed (S207). If a predetermined time has passed(YES in S207), the transmitting station transmits another type of IDsignal depending on what kind of change has been detected (S208). In theexample shown in FIG. 12, a type-c ID signal is transmitted whenacceleration or a change in motion has been sensed, and a type-d IDsignal is transmitted when the sensor 26 detects a change in incidentlight. Similarly, type-e and type-f ID signals are transmitted whendetecting changes in temperature and humidity, respectively. In thisexample, the third ID signal generated by the sensor output containsdifferent types of identifiers corresponding to the environmentalfactors.

[0146] By causing the transmitting station to transmit an ID signal inresponse to the activation signal, the position of that targettransmitting station can be estimated when it is actually required,without consuming the battery power of the transmitting station. Bycausing the transmitting station to generate different types of IDsignals depending on the detected changes, the change in the environmentsurrounding the transmitting station can be known, and consequently, theestimation accuracy and efficiency are improved.

[0147]FIG. 13 illustrates the operation flow of the receiving station 31according to the second embodiment of the invention. When transmissionof an activation signal is required (YES in S211), the receiving station31 transmits an activation signal to the transmitting station (S212).Whenever the receiving station receives an ID signal in response to theactivation signal, it is determined whether the received signal is of atype-a (S213). If a type-a ID signal is received in response to theactivation signal (YES in S213), the intensity of the type-a ID signalis measured (S214). The receiving station also receives other types ofID signals from transmitting stations regardless of the activationsignal. Accordingly, it is determined whether other types of ID signalshave been received (S215). If other types of ID signals have beenreceived (YES in S215), the intensities of these ID signals are measured(S216), and the identifiers are read from the ID signals. Theintensities measured in steps S214 and S216 are supplied to the server12, together with the time stamps, the identifiers read from the IDsignals, and the identifier of the receiving station itself. The timestamp may be created by the server 12 when the signal information isreceived by the server 12.

[0148]FIG. 14 illustrates the operation flow of the positioning computer11 according to the second embodiment of the invention. The positioningcomputer 11 checks time stamps of data stored in the server 12 anddetermines whether a predetermined amount of time has passed (S231). Thepositioning computer also compares the current data with the previousdata (S232) to determine if the current data have been updated (S233) Ifthere are data elements updated from the previous ones (YES in S233),data of fixed-position transmitting stations (T1-T4 in example shown inFIG. 14) whose positions are known in advance are extracted from all theupdated data (S234).

[0149] Using the data of the fixed-position transmitting stations, afirst correcting formula

e _(ij) =S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)

[0150] that defines a relation between intensity (or propagationcharacteristic of the electromagnetic field) e_(ij) and distance d_(ij)is determined. To be more precise, correcting coefficients S1, S2 andenvironmental coefficient Krj are determined so as to minimize Equation(3) (S235) $\begin{matrix}{q = {\sum\limits_{j = 1}^{rn}{\sum\limits_{i = 1}^{tn}{( {e_{ij} - {{\overset{\Cap}{S}}_{1}{\log_{10}( d_{ij} )}} - {\overset{\Cap}{S}}_{2} + {\overset{\Cap}{K}}_{rj}} )^{2}.}}}} & (3)\end{matrix}$

[0151] Then, the relation defined by Equation (4) is assumed for theother (unknown) transmitting stations T5-T8, and Equation (5) is solvedusing the determined formula, with respect to the data of unfixedtransmitting stations (T5-T8), to estimate the positions of thesetransmitting stations (S236). $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj} + K_{ti}})}/S_{1}}} & (4) \\{h_{i} = {\sum\limits_{j = 1}^{rn}( {10^{{({e_{ij} - S_{2} + K_{rj} + {\overset{\Cap}{K}}_{ti}})}/S_{1}} - \sqrt{( {{\overset{\Cap}{x}}_{i} - u_{j}} )^{2} + ( {{\overset{\Cap}{y}}_{i} - v_{j}} )^{2}}} )^{2}}} & (5)\end{matrix}$

[0152] The estimated positions are stored in the server 12. Theestimated positions are compared with the previous results to selectthose transmitting stations whose positions have been changes apredetermined value or more (YES in S237) and those transmittingstations whose signals were not received at any of the receivingstations (YES in S238). The data of the selected transmitting stationsare recorded in the server 12 (S239), and an alert message is suppliedto the associated user terminal (S240).

[0153] Examples of data structures in the server 12 of the secondembodiment are shown in Tables 3 and 4. Table 3 shows a data structureof storing signal information supplied from receiving stations, andTable 4 shows a data structure of storing the estimation resultssupplied from the positioning computer 11. TABLE 3 DATA STRUCTURE OFSIGNAL INFORMATION SUPPLIED FROM RECEIVING STATION RS ID TS ID ID TYPETIME STAMP INTENSITY 0001 0015 c 16:33:10 24

[0154] TABLE 4 DATA STRUCTURE OF ESTIMATION RESULTS SUPPLIED FROMPOSITIONING COMPUTER ID ESTIMATION TR ID TYPE TIME STAMP (X, Y) ENV'LCOEFF. 0015 c 17:22:21 11.95, 9.25 32.4

[0155] Environmental coefficient Kti reflects the environmentsurrounding a transmitting station, and it provides useful informationwhen actually trying to determine the location of the transmittingstation. If the environmental coefficient is large, it indicates thatthe transmitting station is located at an obstructed place with respectto the receiving station. If the environmental coefficient is small, thetransmitting station is located at an open space or an unobstructedplace. Adding such environmental information to the estimated positionallows the user to actually locate the target transmitting station.

[0156] Since in the second embodiment different types of identifiers areconferred on ID signals depending on factors causing ID signals to begenerated, estimation accuracy for unknown transmitting stations isfurther improved as compared with the first embodiment. In addition, atype-a ID signal is generated in response to the activation signal,which is supplied from the receiving station in this embodiment.Consequently, the time interval for transmitting a periodic ID signal(i.e., type-b ID signal) can be made longer. This arrangement can reducethe power consumption of the transmitting station.

[0157] Information of not receiving a signal from a certain transmittingstation can be effectively used as a restrictive condition, as in thefirst embodiment. For example, a signal from transmitting station T2 isreceived at receiving stations R1, R2, and R3, but is not received atR4. In this case, restrictive conditions

[0158] d21<d24

[0159] d22<d24

[0160] d23<d24

[0161] are added. Thus, even unknown information is not discarded, andinstead, it is effectively used in position estimation. The transmittingstation is not limited to a tag, and a transmitting function of a radiodevice, such as a cellular phone and a mobile terminal, may be utilized.

[0162] <Modification 1>

[0163]FIGS. 15 and 16 illustrate a first modification (Modification 1)of the locating system of the second embodiment. In Modification 1, thereceiving station 31 transmits activation signals via ultrasonic waves,while the transmitting station 21 generates and transmits a type-a IDsignal via electromagnetic waves (e.g., radio waves) when receiving theactivation signals. The other structure of the transmitting station 21is the same. Accordingly, when sensing any changes caused by externalfactors, the transmitting station 21 generates ID signals containingdifferent types of identifiers corresponding to the kinds of detectedchanges.

[0164] When receiving an ID signal from the transmitting station 21, thereceiving station 31 measures the intensity of the ID signal and readsthe identifier. The measured intensity and the identifiers of thetransmitting station and the receiving station itself are supplied tothe server 12, together with time stamps. (Time stamps may be created bythe server 12.)

[0165] The positioning computer 11 uses a correcting algorithm as to therelation between propagation characteristic of the electromagnetic field(i.e., the intensity of a received ID signal) and distance. Theoperation flow of the positioning computer 11 is the same as that shownin FIG. 14.

[0166] <Modification 2>

[0167]FIGS. 17 and 18 illustrate a second modification (Modification 2)of the second embodiment. In Modification 2, the receiving station 31transmits activation signals via electromagnetic waves, while thetransmitting station 21 generates and transmits type-a ID signals viaultrasonic waves in response to the activation signals.

[0168] The receiving station 31 measures the intensity of the ID signalcarried by ultrasonic waves, reads the identifier, and supplies themeasured intensity and the identifier to the server 12. The positioningcomputer 11 determines a first correcting formula defining a relationbetween propagation characteristics of ultrasonic wave (i.e., intensity)and distance, and estimates the position of an unknown transmittingstation using the determined formula according to the algorithm shown inFIG. 14. The algorithm shown in FIG. 14 is equally applicable to signalscarried by electromagnetic waves and ultrasonic waves.

[0169] Accordingly, when a signal is transmitted from an i^(th)transmitting station at (xi, yi) via ultrasonic waves and received at aj^(th) receiving station at (uj,vj), the intensity e_(ij) of theultrasonic signal is measured at the j^(th) receiving i^(th) station.The distance between the i^(th) transmitting station and the j^(th)receiving station is expressed by Equation (1).

d _(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j))²)}  (1)

[0170] Then, a first correcting formula defining a relation between theintensity of an ultrasonic signal and distance is determined using theactually measured intensity and known position information. Theintensity of an ultrasonic signal propagating through the air attenuatesas the distance increases because of a spherical diffusion loss due todiffraction and an energy loss absorbed by the medium (i.e., the air).Accordingly, the intensity of an ultrasonic signal has a logarithmicrelation with a distance, and Equation (2) is defined.

e _(ij) =S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)

[0171] where S1, S2 are correcting coefficients and Krj is anenvironmental coefficient for the receiving station. The environmentalcoefficient Krj is an index indicating how the sensitivity of thereceiving station changes from the ideal condition.

[0172] At this stage, the intensity e_(ij) is the intensity of theultrasonic signal transmitted from each of the transmitting stationsT1-T4 whose positions are known in advance and measured at a receivingstation “j”. The solutions for the unknown parameters (S1, S2, and Krj)that minimize an error are obtained by minimizing an estimation functionq expressed by Equation (3). $\begin{matrix}{q = {\sum\limits_{j = 1}^{rn}{\sum\limits_{i = 1}^{tn}( {e_{ij} - {{\overset{\Cap}{S}}_{1}{\log_{10}( d_{ij} )}} - {\overset{\Cap}{S}}_{2} + {\overset{\Cap}{K}}_{rj}} )^{2}}}} & (3)\end{matrix}$

[0173] where rn is the number of known receiving stations, and tn is thenumber of known transmitting stations. In order to solve all theunknows, rn×tn≧rn+2 must stand. In the example shown in FIG. 17, rn isfour, and tn is four. Therefore, all the unknowns can be solved.

[0174] Then, an environmental coefficient Kti for the transmittingstation is introduced, and the relation defined by Equation (4) isassumed for the other (unknown) transmitting stations T5-T8, using thedetermined values of S1, S2 and Krj. $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj} + K_{ti}})}/S_{1}}} & (4)\end{matrix}$

[0175] where md_(ij) is a distance derived from the measured intensitiesof the ultrasonic signals. The position of an unknown transmittingstation “i” and the environmental coefficient Kti are determined byminimizing an estimation function hi expressed by Equation (5), as inthe case using electromagnetic waves. $\begin{matrix}{h_{i} = {\sum\limits_{j = 1}^{rn}( {10^{{({e_{ij} - S_{2} + K_{rj} + {\overset{\Cap}{K}}_{ti}})}/S_{1}} - \sqrt{( {{\overset{\Cap}{x}}_{i} - u_{j}} )^{2} + ( {{\overset{\Cap}{y}}_{i} - v_{j}} )^{2}}} )^{2}}} & (5)\end{matrix}$

[0176] The estimated positions are stored in the server 12. Unknowninformation about an ultrasonic signal that is not received at a certainreceiving station is used as a restrictive condition.

[0177]FIG. 19 illustrates the operation flow of the positioning computer11 in Modification 2. The same steps as those in FIG. 14 usingelectromagnetic waves are denoted by the same numerical references. Thepositioning computer 11 checks time stamps of data stored in the server12 and determines whether a predetermined amount of time has passed(S231). This step is carried out in order to prevent overlooking becausethe transmitting station operates discontinuously, and because IDsignals may not be received due to signal overlap. If a predeterminedtime has passed (YES in S231), the positioning computer 11 compares thecurrent data with the previous data on time-stamp-basis for each type ofidentifier (S232). If there are data elements updated from the previousones (YES in S233) data of fixed-position transmitting stations (T1-T4in example shown in FIG. 19) whose positions are known in advance areextracted from all the updated data (S234).

[0178] Then, Krj, S1, and S2 that minimize Equation (3) are obtained todetermine the first correcting formula as to the relation between theultrasonic wave propagation characteristic and distance (S241). Usingthe determined formula about the ultrasonic wave propagationcharacteristic, the positions of unknown transmitting stations areestimated by solving Equation (5) with respect to data of the othertransmitting stations (T5-T8) (S243). The estimated positions are storedin the server 12.

[0179] The estimated positions are compared with the previous results toselect those transmitting stations whose positions have been changes apredetermined value or more (YES in S237) and those transmittingstations whose signals were not received at any of the receivingstations (YES in S238). The data of the selected transmitting stationsare recorded in the server 12 (S239), and an alert message is suppliedto the associated user terminal (S240).

[0180] The data structures recording signal information from thereceiving station and estimation results supplied from the positioningcomputer 11 in the server 12 are the same as those shown in Tables 3 and4. The structure and the operation of the user terminal 3 are the sameas those described in the first embodiment.

[0181] <Modification 3>

[0182]FIGS. 20 and 21 illustrate a third modification (Modification 3)of the second embodiment. In Modification 3, the receiving stationtransmits an activation signal via ultrasonic waves, and thetransmitting station 21 generates and transmits a type-a ID signal viaultrasonic waves in response to the activation signal.

[0183] The receiving station 31 measures the intensity of the ultrasonicsignal, and supplies the measuring result to the server 12, togetherwith the identifier contained in the received ultrasonic signal. Theoperation flow of the positioning computer 11 is the same as that inModification 2, and the explanation for it will be omitted.

[0184] In the second embodiment, activation signals are supplied fromthe receiving station 31 in order to cause each transmitting station 21to transmit an ID signal. The arrangement allows the system to obtainnecessary position information when it is actually required, whileextending the life of the power source. In addition, the transmittingstation 21 generates and transmits other types of ID signal whendetecting any changes due to environmental or external factors, such asa change in vibration (acceleration), incident light, temperature, andhumidity. This allows the system to estimate the position of atransmitting station more accurately taking the surrounding environmentinto account.

[0185] [Third Embodiment]

[0186]FIG. 22 is a schematic diagram of the locating system according tothe third embodiment of the invention, and FIG. 23 illustrates thetransmitting station 21 and the receiving station 31 used in the thirdembodiment. In the third embodiment, the receiving station 31 has ameans for measuring a transmission time required to acquire a type-a IDsignal in response to the activation signal. Accordingly, as illustratedin FIG. 22, the receiving station R1 measures a transmission time t51required to acquire the ID signal from transmitting station T5, inaddition to the intensity e51. The other fixed-position receivingstations R2-R4 also measure the intensity and the ID signal transmissiontime.

[0187] In the third embodiment, a second correcting formula defining arelation between signal propagation time through the air and distance isused. By using the second correcting formula, the position of atransmitting station can be estimated more accurately. The ID signal istransmitted by electromagnetic waves in the third embodiment.

[0188] The server 12 stores and manages the intensity data and thetransmission time supplied from the receiving station 31, in associationwith the identifier of the transmitting station 21 read from the IDsignal. The positioning computer 11 determines a propagation time of theelectromagnetic signal through the air between the transmitting station21 and the receiving station 31, based on the measured transmissiontime, using correcting coefficients. Then, the positioning computer 11estimates the position of a transmitting station from a ratio of aprescribed proportional constant to the propagation time. Since in thethird embodiment the propagation rate of the signal is corrected fromthe actually measured transmission time using an approximate function,it is not necessary to measure the temperature or the humidity of theair for correction.

[0189] The transmitting station 21 of the third embodiment has the samestructure as that in the second embodiment. The transmitting station 21has a microcontroller 22, a transmitter 23, an ID signal generator 25,and a sensor 26. The ID signal generator 25 periodically generates an IDsignal containing a unique identifier (ID) of that transmitting station21. The microcontroller 22 controls the operation of the transmittingstation 21, and has built-in memories, such as ROM and RAM. The receiver24 receives the activation signal transmitted from the receiving stationand supplies the activation signal to the ID signal generator 25. Thesensor 26 detects changes in various parameters, which are caused byexternal factors 27, and supplies the detection result to the ID signalgenerator 25.

[0190] The transmitting station 21 sets a long oscillation period,regardless of the ON/OFF operation of the sensor 26. The oscillationperiod does not have to be perfectly constant. By randomly varying theoscillation period by several percentages of the period, signalcollision transmitted from different stations can be avoided.

[0191] The ID signal generator 25 generates different types of IDsignals depending on the factors that cause the transmitting station 21to generate ID signals. When receiving an activation signal from areceiving station 31, the ID signal generator 25 generates a type-a IDsignal. A type-b ID signal is also generated based on the periodicoscillation. A type-c ID signal is generated when acceleration or achange in motion has been sensed by the sensor 26. When changes inincident light, temperature, and humidity are sensed, a type-d, type-e,and type-f ID signals are generated, respectively.

[0192] The receiving station 31 has a microcontroller 32, a receiver 33,a transmitter 34, an activation signal generator 35, an anti-collisiondetermination unit 36, and a time computation unit 37. Themicrocontroller 32 controls the operation of the receiving station 31and has built-in memories, such as ROM and RAM. The activation signalgenerator 35 generates an activation signal in a periodic manner. Thereceiver 33 receives first through third ID signals and measures theintensities of the respective signals. The anti-collision determinationunit 36 reads the identifiers (first, second, and third identifiers)from the respective types of ID signals. The time computation unit 37measures the transmission time required to acquire the ID signal inresponse to the activation signal. The transmission time is the timetaken from generation of the activation signal to reading of theidentifier from the received ID signal in this embodiment. The timecomputation unit 37 may be arranged between the transmitter 34 and thereceiver 33. In this case, the transmission time is a time taken fromtransmission of the activation signal to receipt of the ID signal.

[0193] <Algorithm for Correcting Transmission Time>

[0194] As has been mentioned above, the positioning computer 11determines a second correcting formula defining a relation betweensignal propagation time through the air and distance, using correctingcoefficients, based on the transmission time measured by the receivingstation 31.

[0195] In the examples shown in FIG. 22, transmitting stations T1-T4 areattached to the receiving station R1-R4, and their positions are knownin advance. The positions of the transmitting stations T1-T4 areregarded as the same positions as the receiving stations R1-R4.Transmitting stations T5-T8 are unfixed, and their positions areunknown.

[0196] If a known position of the j^(th) receiving station is (uj,vj)and if a position of the i^(th) transmitting station is (xi,yi), thenthe distance between the i^(th) transmitting station and the j^(th)receiving station is expressed by Equation (1).

d _(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j))²)}  (1)

[0197] First, transmission time t_(ij), required to acquire the IDsignal from a transmitting station, is corrected using known positioninformation of the fixed-position receiving stations. The transmissiontime t_(ij) is the sum of a propagation time p_(ij) of the signal(electromagnetic wave in this embodiment) through the air, a signalpropagation time A in the receiving station, and a signal propagationtime b in the transmitting station.

t _(ij) =p _(ij) +A+b  (6)

[0198] Among the terms in the right-hand side, propagation time A in thereceiving station 31 can be regarded as constant among the receivingstations because a high-speed receiving operation is realized using asufficient power source. In contrast, the propagation time b in thetransmitting station 21 has a strong correlation with the intensitye_(ij) because of the reversibility of propagation depending on theconfiguration of the activation signal detection circuit (not shown) ofeach transmitting station. The correlation varies depending on thetechnique for detecting the activation signal, and an approximateformula using a polynomial or an exponential function can be applied.For example, receipt of the activation signal is sensed by a diode,charging a capacitor. Then, it can be regarded that the activationsignal has been detected when the voltage reaches a predetermined level.In this case, an approximate formula defined by Equation (7) is assumedusing an exponential function, which describes the correlation betweenintensity e_(ij) and propagation time b in the transmitting station.

b=f+g exp(−h×e _(ij))  (7)

[0199] In Equation (7), f, g, and h are correcting coefficients.Equation (7) is inserted in Equation (6) to obtain Equation (8).

t _(ij) =p _(ij) +A+f+g exp(−h×e _(ij))  (8)

[0200] Since distance d_(ij) between the transmitting station 21 and thereceiving station 31 is proportional to signal propagation time p_(ij)through the air, Equation (8) is modified as Equation (9).

p _(ij) =t _(ij) −A−f−g exp(−h×e _(ij))=Kd _(ij)  (9)

[0201] Equation (9) is the second correcting formula, where K is aproportional constant.

[0202] At this stage, e_(ij) is the intensity of the ID signaltransmitted from each of transmitting stations T1-T4 whose positions arealready known (referred to as “known transmitting stations”). Unknownparameters are five, that is, A, F, g, h and K. If A and f areconsidered as a single parameter B (=A+f), then the number of unknownsbecomes four. The solutions for these unknowns that minimize the errorare obtained by minimizing estimation function qq expressed by Equation(10). $\begin{matrix}{{qq} = {\sum\limits_{j = 1}^{rn}{\sum\limits_{i = 1}^{tn}( {t_{ij} - \overset{\Cap}{B} - {\overset{\Cap}{g}\quad {\exp ( {{- \overset{\Cap}{h}} \times e_{ij}} )}} - {\overset{\Cap}{K}\quad d_{ij}}} )^{2}}}} & (10)\end{matrix}$

[0203] where rn is the number of the receiving stations whose positionsare known (referred to as “known receiving stations”), and tn is thenumber of known transmitting stations. In order to solve all theunknowns, rn×tn≧4 must be satisfied. In the example shown in FIG. 22, rnis four and tn is four, and therefore, all the unknowns can be solved.For the purpose of clarification, unknowns are marked with an arc abovethe symbols.

[0204] There are many known methods for solving Equation (10). Forexample, partially differentiating function qq with respect to eachvariable, and obtaining the numerical solutions that make the respectivepartial differentials zero using, for example, the Newton method.Alternatively, the simplex method, the steepest descent method (orsaddle point method), methods using neural networks can be used. Usingany one of these methods, the correcting coefficients B, g and h, aswell as proportional constant K for the signal propagation time p_(ij)and distance d_(ij), are determined.

[0205] Distance nd_(ij) from an unknown transmitting station to a knownreceiving station can be derived using the signal propagation timep_(ij) determined by Equation (10). The relation between nd_(ij) andp_(ij) is expressed by Equation (11) using proportional constant K.$\begin{matrix}{{nd}_{ij} = {{p_{ij}/K} = {\{ {t_{ij} - B - {g\quad {\exp ( {{- h} \times e_{ij}} )}}} \}/K}}} & (11)\end{matrix}$

[0206] where nd_(ij) is a distance derived from the actually measuredtransmission time. The position of the i^(th) unknown transmittingstation can be determined by minimizing estimation function hhiexpressed by Equation (12). $\begin{matrix}{{hh}_{i} = {\sum\limits_{j = 1}^{rn}( {{\{ {t_{ij} - B - {g\quad {\exp ( {{- h} \times e_{ij}} )}}} \}/K} - \sqrt{( {{\overset{\Cap}{x}}_{i} - u_{j}} )^{2} + ( {{\overset{\Cap}{y}}_{i} - v_{j}} )^{2}}} )^{2}}} & (12)\end{matrix}$

[0207] For the purpose of clarification, unknowns are marked with an arcabove the symbols in Equation (12). With the method described above, theposition (xi, yi) of the i^(th) unknown transmitting station can beestimated from the measured transmission time.

[0208] Using the estimated position of the unknown transmitting station,the estimation accuracy for environmental coefficient Kti for thistransmitting station can also be improved.

[0209] First, as in the second embodiment, environmental coefficient Krjfor receiving station j is defined. The environmental coefficient Krj isan index indicating how the sensitivity of the receiving stationdeviates from the ideal state. Similarly, environmental coefficient Ktifor transmitting station i is defined.

[0210] The relation between the intensity of a received signal anddistance is corrected using corrected Friis' formula (i.e., the firstcorrecting formula) using position information of known receivingstations. The first correcting formula defining a relation betweenintensity e_(ij) and distance d_(ij) is determined using actuallymeasured values between the known transmitting stations T1-T4 and knownreceiving stations R1-R4. It is assumed that the intensity has alogarithmic relation with distance, and Equation (2) is assumed.

e _(ij) =S ₁×log₁₀(d _(rj))+S ₂ −K _(rj)  (2)

[0211] where S1 and S2 are correcting coefficients. At this stage,intensity e_(ij) is the intensity of an ID signal transmitted from eachof known transmitting station T1-T4 and measured at each of knownreceiving stations R1-R4. The solutions for the unknowns in Equation (2)that minimize the error can be obtained by minimizing estimationfunction q expressed by Equation (3). $\begin{matrix}{q = {\sum\limits_{j = 1}^{rn}{\sum\limits_{i = 1}^{tn}( {e_{ij} - {{\overset{\Cap}{S}}_{1}{\log_{10}( d_{ij} )}} - {\overset{\Cap}{S}}_{2} + {\overset{\Cap}{K}}_{rj}} )^{2}}}} & (3)\end{matrix}$

[0212] where rn is the number of known receiving stations and tn is thenumber of known transmitting stations. In order to solve all theunknowns, rn×tn≧4 must be satisfied. In the example shown in FIG. 22, rnis four and tn is four, and therefore, all the unknowns can be solved.For the purpose of clarification, unknowns are marked with an arc abovethe symbols.

[0213] Solutions for Equation (3) can be obtained by, for example,partially differentiating function q with respect to each variable andobtaining the numerical solutions that make the respective partialdifferentials zero using the Newton method. Alternatively, the simplexmethod, the steepest descent method (or saddle point method), methodsusing neural networks can be used, as in the second embodiment. Usingany one of these methods, the correcting coefficients S1 and S2 aredetermined.

[0214] Next, environmental coefficient Kti for unknown transmittingstation is introduced. Although the transmitting intensity at atransmitting station is constant, the environmental coefficient variesdepending on the location, and therefore, the intensity of the receivedsignal varies. Accordingly, a relation between intensity and distance isassumed as Equation (4) introducing environmental coefficient Kti fortransmitting station, in addition to the correcting coefficients S1, S2and the environmental coefficient Krj for the receiving stationdetermined by Equation (3). $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj} + K_{ti}})}/S_{1}}} & (4)\end{matrix}$

[0215] where md_(ij) is a distance derived from the measured intensity.The environmental coefficient Kti can be obtained by minimizingestimation function hhhi expressed by Equation (13). $\begin{matrix}{{hhh}_{i} = {\sum\limits_{j = 1}^{rn}( {10^{{({e_{ij} - S_{2} + K_{rj} + {\overset{\Cap}{K}}_{ti}})}/S_{1}} - \sqrt{( {x_{1} - u_{j}} )^{2} + ( {y_{1} - v_{j}} )^{2}}} )^{2}}} & (13)\end{matrix}$

[0216] For the purpose of clarification, the unknown is marked with anarc above the symbols. As the position (xi, yi) of the transmittingstation, the values estimated by Equation (12) using the correctingalgorithm for transmission time is used. In this manner, the estimationaccuracy for the environmental coefficient Kti for transmitting stationi is improved.

[0217] As in the first and second embodiments, information that an IDsignal is not received at a certain receiving station is used as arestrictive condition. Thus, unknown information is effectively utilizedin position estimation.

[0218]FIG. 24 illustrates the operation flow of the receiving station 31according to the third embodiment. At a timing for transmitting anactivation signal (YES in S311), the receiving station 31 transmits anactivation signal to the transmitting station 21 (S312). Then, whenreceiving an ID signal from the transmitting station in response to theactivation signal, it is confirmed if the received signal is a type-a IDsignal (S313). If a type-a ID signal has been received (YES in S313), atransmission time required to acquire the ID signal (e.g., the timerequired to read the identifier since generation of the activationsignal) is measured (S314). The intensity of the received ID signal isalso measured (S315). The measured transmission time and the intensityare supplied to the server 12, together with the identifier of thetransmitting station, the identifier of the receiving station itself,and time stamp (S316). The time stamp may be created by server 12.

[0219] The transmitting station transmits ID signals not only whenreceiving an activation signal, but also when detecting changes due toexternal factors. Accordingly, the receiving station determined whetherother types of ID signals have been received (S317). If an ID signalother than type-a ID signal has been received (YES in S317), theidentifier is read from the ID signal, and the intensity of the IDsignal is measured (S318). The measured intensity, the identifier of thetransmitting station, and the identifier of the receiving station itselfare supplied to the server 12, together with a time stamp (S319).

[0220]FIG. 25 illustrates the operation flow of the positioning computer11 according to the third embodiment. The positioning computer 11 checkstime stamps of data stored in the server 12 and determines whether apredetermined amount of time has passed (S331). This step is carried outin order to prevent overlooking because the transmitting stationoperates discontinuously and because the ID signals may not be receiveddue to signal overlap. Then, based on the time stamps, the current dataare compared with the previous data for each identifier (S332) todetermine if the current data have been updated (S333). If there aredata elements updated from the previous ones (YES in S333), data offixed-position transmitting stations (T1-T4 in example shown in FIG. 22)whose positions are known in advance are extracted from all the updateddata (S334).

[0221] Using the data of the fixed-position transmitting stations,correcting coefficients B, g, h and proportional constant K for ratio ofp_(ij) (signal propagation time through the air) to d_(ij) (distance)that minimize Equation (10) are determined (S335). In addition,correcting coefficients S1, S2 and environmental coefficient Krj thatminimize Equation (3) are determined to provide a propagation formulafor the electromagnetic field (S336).

[0222] Then, positions of the data-updated transmitting stations areestimated using appropriate algorithms depending on the case in which

[0223] 1) the identifier read from the ID signal is of type a (that is,the ID signal is transmitted in response to the activation signal); or

[0224] 2) the identifier read from the ID signal is one of types b-f(that is, the ID signal is transmitted spontaneously by periodicoscillation or detection of changes).

[0225] Accordingly, it is determined if the ID signal from thedata-updated transmitting station is of type a (S337). If the ID signalis of type a (YES in S337), Equation (12) is solved to estimate theposition of the transmitting station from the measured transmission time(S338). The estimation result is stored in the server 12. Then, Equation(13) is solved to determine the environmental coefficient Kti for thetransmitting station from the estimated position and the measuredintensity (S339). The determined environmental coefficient Kti is alsostored in the server 12.

[0226] On the other hand, if the ID signal from the data-updatedtransmitting station is one of types b-f (NO in S337), Equation (13) issolved with the position of the transmitting station as an unknownparameter to estimate the position of the transmitting station and theenvironmental coefficient (S340). The estimation result is stored in theserver 12.

[0227] If there are any other updated data (YES in S341) steps S337through S340 are repeated to estimate the position of the transmittingstation and environmental coefficient for the update data. If there isno more data-updated transmitting station (NO in S341), the estimationresults are compared with the previous results to select thosetransmitting stations whose positions have been changes a predeterminedvalue or more (YES in S342) and those transmitting stations whosesignals were not received at any of the receiving stations (YES inS343). The data of the selected transmitting stations are recorded inthe server 12 (S344), and an alert message is supplied to the associateduser terminal (S345).

[0228] Table 5 shows an example of a data structure recording data fromthe receiving station in the server 12, and Table 6 shows an example ofa data structure recording estimation result supplied from thepositioning computer 11. TABLE 5 DATA STRUCTURE OF SIGNAL INFORMATIONSUPPLIED FROM RECEIVING STATION RS ID TR ID ID TYPE TIME STAMPTRANSMISSION TIME INTENSITY 0001 0015 a 16:33:10 00:00:00000080 24 00010015 c 17:33:10 23

[0229] TABLE 6 DATA STRUCTURE OF ESTIMATION RESULTS SUPPLIED FROMPOSITIONING COMPUTER ID ESTIMATION TR ID TYPE TIME STAMP (X, Y) ENVIR'LCOEFF. 0015 a 17:22:21 11.34, 9.15 31.0 0015 c 18:22:21 11.95, 9.25 32.4

[0230] Environmental coefficient Kti reflects the environmentsurrounding a transmitting station, and it provides useful informationwhen actually trying to determine the location of the transmittingstation. If the environmental coefficient is large, it indicates thatthe transmitting station is located at an obstructed place with respectto the receiving station. If the environmental coefficient is small, thetransmitting station is located at an open space or an unobstructedplace. Adding such environmental information to the estimated positionallows the user to actually locate the target transmitting station.

[0231] The user terminal 3 has two functions, as in the first and secondembodiments, that is, receiving an alert message supplied from thepositioning computer 11, and retrieving the position of a targettransmitting station. The user inputs the identifier (ID) of the targettransmitting station into the user terminal. The user terminal accessesthe server 12 to retrieve in the server 12 the past record of thatidentifier, such as time stamps, position information, environmentalcoefficient, etc. The retrieved result is displayed on the userterminal.

[0232] The user can determine whether the target transmitting station islocated at an open space from the position information described by timestamps and the corresponding environmental coefficient. In addition, theuser can determine when an activation signal is received at thetransmitting station or when external change has been detected from thepast record.

[0233] In the third embodiment, a transmission time required to acquirean ID signal is used, together with the intensity of the received IDsignal, to estimate the position of a transmitting station. Theestimation result is more accurate as compared with the case using theintensity only.

[0234] Since when defining a second correcting formula, the signalpropagation time through the air is corrected from the actually measuredvalues using an approximate function, it is not necessary to measure thetemperature and the humidity in the air for the correction.

[0235] The relation between the intensity and time is also correctedfrom the actually measured value using an approximate function.Accordingly, the estimation accuracy is still improved even if areceiving station cannot perform high-speed receiving operation forreducing power consumption.

[0236] [Fourth Embodiment]

[0237]FIG. 26 illustrates a locating system according to the fourthembodiment of the invention, and FIG. 27 illustrates the structures ofthe transmitting station 21 and the receiving station 31 used in thesystem shown in FIG. 26. In the fourth embodiment, a receiving stationR1 fixed at a known position (hereinafter referred to as “fixed-positionreceiving station”), and another receiving R2 station that moves freely(hereinafter referred to as “moving receiving station”) are used toestimate the positions of plural transmitting stations.

[0238] As shown in FIG. 26, a locating system includes a fixed-positionreceiving station (or a first receiving station R1) 51 a, a movingreceiving station (or a second receiving station R2) 51 b, transmittingstations 21 (T1-T8), a positioning computer 11, and user terminals 3.The positioning computer 11, the server 12, and the user terminals 3 aremutually connected via LAN 2. Since a moving receiving station R2 isused in the fourth embodiment, the receiving stations 51 are connectedto the server 12 via a wireless network. For this reason, the server 12has a wireless LAN base station 41. Each of the receiving stations 51 aand 51 b also has a wireless LAN cellular station 40.

[0239] Each of the receiving stations 51 a and 51 b has amicrocontroller 32, a receiver 33, a transmitter 34, an activationsignal generator 35, an anti-collision determination unit 36, and a timecomputation unit 37. The microcontroller 32 controls the operation ofthe receiving station 51 and has built-in memories, such as ROM and RAM.The activation signal generator 35 generates an activation signal, andthe transmitter 34 transmits the activation signal to transmittingstations. The receiver 33 receives an ID signal from each transmittingstation and measures the intensity of the received ID signal. Theanti-collision determination unit 36 reads or extracts the identifierfrom the ID signal. The time computation unit 37 measures a transmissiontime required to acquire the ID signal. In the fourth embodiment,transmission time is the time required to read the identifier since thegeneration of the activation signal. However, the time computation unit37 may be connected between the transmitter 34 and the receiver 33. Inthis case, the transmission time is the time required to receive the IDsignal since transmission of the activation signal.

[0240] The transmitting station 21 has the same structure as illustratedin the second and third embodiments. Namely, the transmitting station 21has a microcontroller 22, a transmitter 23, an ID signal generator 25,and a sensor 26. The ID signal generator 25 periodically generates an IDsignal containing a unique identifier (ID) of that transmitting station21. The microcontroller 22 controls the operation of the transmittingstation 21, and has built-in memories, such as ROM and RAM. The receiver24 receives the activation signal transmitted from the receiving stationand supplies the activation signal to the ID signal generator 25. Thesensor 26 detects changes in various parameters, which are caused byexternal factors 27, and supplies the detection result to the ID signalgenerator 25. The ID signal generator 25 generates different kinds of IDsignals when receiving the activation signal from the receiving stationand when detecting a change, in addition to a periodic signal of arelatively long interval. With this arrangement, an ID signal istransmitted when it is actually required, and power consumption of thebattery can be reduced. The size of the log file can also be reduced.The sensor 26 is realized by combining an acceleration sensor using aninverted pendulum, a light sensor, a temperature sensor, a humiditysensor, and other types of sensors.

[0241] The positioning computer 11 estimates the position of atransmitting station based on the data stored in the server 12, usingthe first and second correcting formulas, according to the algorithmdescribed below.

[0242] <Algorithm for Correcting Transmission Time>

[0243] In the example shown in FIG. 26, the positions of transmittingstations T1-T4 are known (and these transmitting stations are referredto as “known transmitting stations”). The fixed-position receivingstation R1 is set at the same position as transmitting station T1, andits position is (u1, v1). The moving receiving position R2 travels withits position changing, as indicated by the dashed arrows. For theconvenience of explanation and estimation, R3 and R4 denote the newpositions of the moving receiving station. The j^(th) position of themoving receiving station R2 is (uj, vj). The positions of transmittingstations T5-T8 are unknown (and these transmitting stations are referredto as “unknown transmitting stations”), and the position of the i^(th)transmitting station is (xi, yi). An ID signal is transmitted from atransmitting station to the receiving stations R1 and R2 viaelectromagnetic waves, and the intensity of the ID signal received atthe receiving station at the j^(th) position (referred to as the j^(th)receiving station for convenience) is e_(ij). The distance between thei^(th) transmitting station and the j^(th) receiving station is d_(ij),which is expressed by Equation (1).

d _(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j))²)}  (1)

[0244] First, transmission time t_(ij), required to acquire the IDsignal and read the identifier, is corrected using known positioninformation of the fixed-position receiving station. The transmissiontime t_(ij) is the sum of a propagation time p_(ij) of the signal(electromagnetic wave in this embodiment) through the air, a signalpropagation time A in the receiving station, and a signal propagationtime b in the transmitting station.

t _(ij) =p _(ij) +A+b  (6)

[0245] Among the terms in the right-hand side, propagation time A in thereceiving station 51 can be regarded as constant among the receivingstations because a high-speed receiving operation is realized using asufficient power source. In contrast, the propagation time b in thetransmitting station 21 has a strong correlation with the intensitye_(ij) because of the reversibility of propagation depending on theconfiguration of the activation signal detection circuit (not shown) ofeach transmitting station. The correlation varies depending on thetechnique for detecting the activation signal, and an approximateformula using a polynomial or an exponential function can be applied.For example, receipt of the activation signal is sensed by a diode,charging a capacitor. Then, it can be regarded that the activationsignal has been detected when the voltage reaches a predetermined level.In this case, an approximate formula defined by Equation (7) is assumedusing an exponential function, which describes the correlation betweenintensity e_(ij) and propagation time b in the transmitting station.

b=f+g exp(−h×e _(ij))  (7)

[0246] In Equation (7), f, g, and h are correcting coefficients.Equation (7) is inserted in Equation (6) to obtain Equation (8).

t _(ij) =p _(ij) +A+f+g exp(−h×e _(ij))  (8)

[0247] Since distance d_(ij) between the transmitting station 21 and thereceiving station 31 is proportional to signal propagation time p_(ij)through the air, Equation (8) is modified as Equation (9).

p _(ij) =t _(ij) −A−f−g exp(−h×e _(ij))=Kd _(ij)  (9)

[0248] Equation (9) is the second correcting formula, where K is aproportional constant.

[0249] At this stage, e_(ij) is the intensity of the ID signaltransmitted from each of transmitting stations T1-T4 whose positions arealready known (referred to as “known transmitting stations”). Unknownparameters are five, that is, A, F, g, h and K. If A and f areconsidered as a single parameter B (=A+f) then the number of unknownsbecomes four. The solutions for these unknowns that minimize the errorare obtained by minimizing estimation function qqq expressed by Equation(14). $\begin{matrix}{{qqq} = {\sum\limits_{j = 1}^{rn}{\sum\limits_{i = 1}^{tn}( {t_{ij} - \overset{\Cap}{B} - {\overset{\Cap}{g}\quad {\exp ( {{- \overset{\Cap}{h}} \times e_{ij}} )}} - {\overset{\Cap}{K}\quad d_{ij}}} )^{2}}}} & (14)\end{matrix}$

[0250] where rn is the number of the receiving stations whose positionsare known, and tn is the number of known transmitting stations. In orderto solve all the unknowns, rn×tn≧4 must be satisfied. In the exampleshown in FIG. 26, rn is one and tn is four, and therefore, all theunknowns can be solved. For the purpose of clarification, unknowns aremarked with an arc above the symbols.

[0251] There are many known methods for solving Equation (14). Forexample, partially differentiating function qqq with respect to eachvariable, and obtaining the numerical solutions that make the respectivepartial differentials zero using, for example, the Newton method.Alternatively, the simplex method, the steepest descent method (orsaddle point method), methods using neural networks can be used. Usingany one of these methods, the correcting coefficients B, g and h, aswell as proportional constant K for the signal propagation time p_(ij)and distance d_(ij), are determined.

[0252] Distance nd_(ij) from an unknown transmitting station to a knownreceiving station can be derived using the signal propagation timep_(ij) determined by Equation (14). The relation between nd_(ij) andp_(ij) is expressed by Equation (15) using proportional constant K.$\begin{matrix}{ {{nnd}_{ij} = {{p_{ij}/K} = {\{ {t_{ij} - B - {g\quad \exp}} )( {{- h} \times e_{ij}} )}}} \}/K} & (15)\end{matrix}$

[0253] where nnd_(ij) is a distance derived from the measuredtransmission time. Then, Equation (3) is solved to determine correctingcoefficients S1, S2 and environmental coefficient Krj for the receivingstation.

[0254] <Algorithm Used When the Moving Receiving Station Travels>

[0255] As the moving receiving station R2 travels to R3, and to R4, thenew position (uj, vj) of the moving receiving station can be estimatedusing position information of at least three known transmitting stationsamong T1-T4, by minimizing estimation function hhhhj expressed byEquation (16). $\begin{matrix}{{hhhh}_{j} = {\sum\limits_{i = 1}^{ttn}( {{\{ {t_{ij} - B - {g\quad {\exp ( {{- h} \times e_{ij}} )}}} \}/K} - \sqrt{( {x_{1} - {\overset{\Cap}{u}}_{j}} )^{2} + ( {y_{1} - {\overset{\Cap}{v}}_{j}} )^{2}}} )^{2}}} & (16)\end{matrix}$

[0256] where ttn is the number of known transmitting stations whoseposition information can be utilized. For clarification, unknows aremarked with an arc above the symbols.

[0257] Then, an activation signal is transmitted from the moving stationlocated at the estimated position to an unknown transmitting station.The position of this unknown transmitting station can be estimated usinginformation about at least three positions of the receiving stations(including the position information of the fixed-position receivingstation R1, and the estimated positions R2, R3 . . . of the movingreceiving station) Position (xi, yi) of the unknown transmitting stationis estimated by minimizing estimation function hhhhhi expressed byEquation (17). $\begin{matrix}{{hhhhh}_{i} = {\sum\limits_{j = 1}^{rrn}( {{\{ {t_{ij} - B - {g\quad {\exp ( {{- h} \times e_{ij}} )}}} \}/K} - \sqrt{( {{\overset{\Cap}{x}}_{1} - u_{j}} )^{2} + ( {{\overset{\Cap}{y}}_{1} - v_{j}} )^{2}}} )^{2}}} & (17)\end{matrix}$

[0258] where rrn is the number of available positions of the receivingstation used for estimation. Unknowns are marked with an arc above thesymbols for clarification.

[0259] <Algorithm Used When Known Transmitting Station is Out of Area>

[0260] As the moving receiving station 51 b travels, the transmittingstations T1-T4 fixed at known positions are out of the communicationarea of the receiving station 51 b. Accordingly, the positions oftransmitting stations T5-T8, which have already been estimated in theabove-described manner, are used to estimate a new position of themoving receiving station 51 b.

[0261] The positions of unknown transmitting stations T5-T8 aresuccessively estimated using the time-correcting algorithm using thesecond correcting formula and the algorithm for moving receivingstation. By making use of the estimated position information, theestimation accuracy for the environmental coefficient Kti for thetransmitting station can be improved.

[0262] Environmental coefficient Krj for the receiving station “j” isdefined. The environmental coefficient Krj is an index indicating howthe sensitivity of the receiving station changes from the idealcondition. Similarly, environmental coefficient Kti for a targettransmitting station is also defined.

[0263] First, the Friis' formula is corrected using correctingcoefficients S1, S2, and an environmental coefficient Krj to define arelation between distance “d” and intensity “e”, using the actuallymeasured values between the transmitting station 21 and the receivingstation 51. Based on the assumption that distance and intensity are inthe logarithmic relation, Equation (2) is defined.

e _(ij) =S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)

[0264] where S1 and S2 are correcting coefficients. At this stage,e_(ij) is the intensity of the ID signal transmitted from a knowntransmitting station whose position has already been estimated. Thesolutions for the unknown parameters that make the error minimum areobtained by minimizing estimation function q expressed by Equation (3).$\begin{matrix}{q = {\sum\limits_{j = 1}^{rn}{\sum\limits_{i = 1}^{tn}( {e_{ij} - {{\overset{\Cap}{S}}_{1}{\log_{10}( d_{ij} )}} - {\overset{\Cap}{S}}_{2} + {\overset{\Cap}{K}}_{rj}} )^{2}}}} & (3)\end{matrix}$

[0265] where rn is the number of receiving stations whose positions areknown, and tn is the number of known transmitting stations. To solve allthe unknowns, un×tn≧rn+2 must be satisfied. In the example shown in FIG.26, rn is one and tn is four, and therefore, all the unknowns aresolved. For clarification, unknowns are marked with an arc above thesymbols.

[0266] There are many methods for solving Equation (3) for example, bypartially differentiating function q with respect to each variable andobtaining the numerical solutions that make the respective partialdifferentials zero using the Newton method. Alternatively, the simplexmethod, the steepest descent method (or saddle point method), methodsusing neural networks can be used. Using any one of these methods, thecorrecting coefficients S1, S2 and environmental coefficient Krj aredetermined.

[0267] Next, environmental coefficient Kti for an unknown transmittingstation is introduced. Although the transmitting intensity at atransmitting station is constant, the environmental coefficient variesdepending on the location, and therefore, a relation between intensityand distance is assumed as Equation (4) introducing environmentalcoefficient Kti for transmitting station. Equation (4) contains thecoefficients S1, S2 and the environmental coefficient Krj for thereceiving station that have been determined by Equation (3).$\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj} + K_{ti}})}/S_{1}}} & (4)\end{matrix}$

[0268] where md_(ij) is a distance derived from the measured intensity.Kti can be determined by minimizing estimation function hhhhhhiexpressed by Equation (18). $\begin{matrix}{{hhhhhh}_{\quad i} = {\sum\limits_{j = 1}^{rn}\quad ( {10^{{({e_{ij} - S_{2} + K_{rj} + {\overset{\Cap}{K}}_{ti}})}/S_{1}} - \sqrt{( {x_{i} - u_{j}} )^{2} + ( {y_{i} - v_{j}} )^{2}}} )^{2}}} & (18)\end{matrix}$

[0269] For clarification, unknowns are marked with an arc above thesymbols. In Equation (18), position (xi, yi) is described usingestimated values which are determined from the measured intensity andtransmission time using Equation (17).

[0270] In the fourth embodiment, the positioning computer 11 carries outthe steps of:

[0271] (1) determining unknowns in the first and second correctingformulas using the actually measured intensity and transmission, as wellas known position information;

[0272] (2) estimating a new position of the moving receiving stationusing the determined values of unknowns and known position information(Algorithm A); and

[0273] (3) estimating a position of an unknown transmitting stationusing known or estimated position information of the moving receivingstation (Algorithm B).

[0274] As the moving receiving station R2 travels, its communicationarea also moves. By repeating Algorithms A and B along with shifting ofthe communication area, the positions and the environmental coefficientsof unknown transmitting stations can be obtained successively in newareas. As a result, high-accuracy position estimation is realized over awide area.

[0275] The estimation results (including the positions of unknowntransmitting stations and new positions of moving receiving station R2)are stored in the server 12. To obtain the position of a targettransmitting station, the user simply inputs the identifier of thetarget transmitting station through the user terminal 3, which is to beretrieved in the server 12 via LAN 2.

[0276] As in the first through third embodiments, when an ID signalcannot be received at a certain receiving station, this unknowninformation is made use of as a restrictive condition. For example, asignal from transmitting station T2 is received at receiving stationsR1, R2, and R3, but is not received at R4. In this case, restrictiveconditions

[0277] d21<d24

[0278] d22<d24

[0279] d23<d24

[0280] are added. Thus, even unknown information is not discarded, andinstead, it is effectively used in position estimation.

[0281]FIG. 28 illustrates the operation flow of the receiving station51. Basically, the fixed-position receiving station 51 a (R1) and themoving receiving station 51 b (R2→R3→R4) carry out the same operation,which is the same as that carried by the receiving station 31 used inthe third embodiment.

[0282] At a timing for transmitting an activation signal (YES in S411),the receiving station 31 transmits an activation signal to thetransmitting station 21 (S412). Then, when receiving an ID signal fromthe transmitting station in response to the activation signal, it isconfirmed if the received signal is a type-a ID signal (S413). If atype-a ID signal has been received (YES in S413), a transmission timerequired to acquire the ID signal (e.g., time for required to read theidentifier since generation of the activation signal) is measured(S414). The intensity of the received ID signal is also measured (S415).The measured transmission time and the intensity are supplied to theserver 12, together with the identifier of the transmitting station, theidentifier of the receiving station itself, and time stamp (S416). Thetime stamp may be created by server 12.

[0283] The transmitting station transmits ID signals not only whenreceiving an activation signal, but also when detecting changes due toexternal factors. Accordingly, the receiving station determines whetherother types of ID signals have been received (S417). If an ID signalother than type-a ID signal has been received (YES in S417), theidentifier is read from the ID signal, and the intensity of the IDsignal is measured (S418). The measured intensity, the identifier of thetransmitting station, and the identifier of the receiving station itselfare supplied to the server 12, together with time stamp (S419).

[0284]FIG. 29 illustrates the operation flow of the positioning computer11 according to the fourth embodiment. The positioning computer 11checks time stamps of data stored in the server 12 and determineswhether a predetermined amount of time has passed (S431). This step iscarried out in order to prevent overlooking because the transmittingstation operates discontinuously and because the ID signals may not bereceived due to signal overlap. Then, based on the time stamps, thecurrent data are compared with the previous data for each identifier(S432) to determine if the current data have been updated (S433). Ifthere are data elements updated from the previous ones (YES in S433),data of fixed-position transmitting stations (T1-T4 in example shown inFIG. 26) whose positions are known in advance are extracted from all theupdated data. Using the data of the fixed-position transmittingstations, correcting coefficients B, g, h and proportional constant Kfor ratio of p_(ij) (signal propagation time through the air) to d_(ij)(distance) that minimize Equation (14) are determined. In addition,correcting coefficients S1, S2 and environmental coefficient Krj thatminimize Equation (3) are determined to provide a propagation formulafor the electromagnetic field (S434).

[0285] (A) Then, data of known or position-estimated transmittingstation are extracted from the data supplied from the receiving stationR2 at an unknown position (S435). It is then determined whether the IDsignal from a data-updated transmitting station is of type a (S436). Ifthe ID signal is of type a (YES in S436), Equation (16) is solved usingthe measured intensity and transmission time required for acquiring theidentifier to estimate the position of the moving receiving station. Theestimation result is stored in the server 12. Furthermore, Equation (3)is solved to determine the environmental coefficient Krj of the movingreceiving station at the estimated position, which is also stored in theserver 12 (S437).

[0286] On the other hand, if the ID signal is one of types b-f (NO inS436), Equation (3) is solved, with the position of the moving receivingstation as an unknown parameter, to estimate the position and theenvironmental coefficient of the receiving station. The estimationresult is stored in the server 12 (S438). The steps 435-438 correspondto Algorithm (A) described above.

[0287] (B) Then, data of an unknown transmitting station is extractedfrom the data supplied from the fixed-position receiving station R1 orfrom the moving receiving station at the estimated positions (R2, R3)(S439). It is determined as to the data-updated transmitting stationwhether the ID signal is of type a (S440). If the ID signal is of type a(YES in S440), Equation (17) is solved using the measured transmissiontime and intensity to estimate the position of the unknown transmittingstation, which is stored in the server 12. Furthermore, Equation (18) issolved to estimate the environmental coefficient Kti for thattransmitting station, which is also stored in the server 12. (S441).

[0288] On the other hand, the ID signal is not of type a (NO in S440),then Equation (18) is solved, with the position of the targettransmitting station as an unknown parameter, to estimate the positionand the environmental coefficient of the target (unknown) transmittingstation. The estimation result is stored in the server 12 (S442). Thesteps S439 through S442 correspond to above-described Algorithm (B).

[0289] Steps S435-S442 (that is, Algorithms (A) and (B)) are repeatedfor all the data-updated transmitting stations (YES in S443). Thecurrent estimation result is compared with the previous one to selectthose transmitting stations that have moved a predetermined amount ormore (YES in S444) and those transmitting stations from which ID signalsare not received at any receiving stations (YES in S445). The selectionresult is stored in the server 12 (S446), and an alert message issupplied to the associated user terminal (S447).

[0290] Table 7 shows an example of a data structure recording the datafrom the receiving station 51 in the server 12, and Table 8 shows anexample of a data structure recording the estimation result suppliedfrom the positioning computer 11. TABLE 7 DATA STRUCTURE OF SIGNALINFORMATION SUPPLIED FROM RECEIVING STATION RS ID TS ID ID TYPE TIMESTAMP TRANSMISSION TIME INTENSITY 0001 0015 a 16:33:10 00:00:00000080 240001 0015 c 17:33:10 23 0001 0015 a 16:33:40 00:00:00000050 14 0001 0016a 16:33:40 00:00:00000061 13 0001 0017 a 16:33:40 00:00:00000070 12 00010018 a 16:33:40 00:00:00000075 14

[0291] TABLE 8 DATA STRUCTURE OF ESTIMATION RESULTS SUPPLIED FROMPOSITIONING COMPUTER ID ESTIMATION TS ID TYPE TIME STAMP (X, Y) ENVIR'LCOEFF. 0015 a 17:22:21 11.34, 9.15 31.0 0015 c 18:22:21 11.95, 9.25 32.4ID ESTIMATION RS ID TYPE TIME STAMP (X, Y) ENVIR'L COEFF. 0002 a17:22:23  5.34, 3.15 10.0 0002 c 18:22:24  6.95, 4.25 12.4

[0292] Environmental coefficient Kti reflects the environmentsurrounding a transmitting station, and it provides useful informationwhen actually trying to determine the location of the transmittingstation. If the environmental coefficient is large, it indicates thatthe transmitting station is located at an obstructed place with respectto the receiving station. If the environmental coefficient is small, thetransmitting station is located at an open space or an unobstructedplace. Adding such environmental information to the estimated positionallows the user to actually locate the target transmitting station.

[0293] The user terminal 3 has two functions, as in the first throughthird second embodiments, that is, receiving an alert message suppliedfrom the positioning computer 11, and retrieving the position of atarget transmitting station. The user inputs the identifier (ID) of thetarget transmitting station into the user terminal. The user terminalaccesses the server 12 to retrieve in the server 12 the past record ofthat identifier, such as time stamps, position information,environmental coefficient, etc. The retrieved result is displayed on theuser terminal.

[0294] The user can determine whether the target transmitting station islocated at an open space from the position information described by timestamps and the corresponding environmental coefficient. In addition, theuser can determine when an activation signal is received at thetransmitting station or when external change has been detected from thepast record.

[0295] In the fourth embodiment, accurate position estimation for alarge number of transmitting stations is realized over a wide area,using a fixed-position receiving station and a moving receiving station.For example, position information about four transmitting stations and areceiving station at known positions are used, while another receivingstation is allowed to move around. Unknown parameters in the first andsecond correcting formulas are determined from the position informationof the known transmitting stations and the known receiving station, andthe measured transmission time and intensity. Then, (A) the position ofthe moving receiving station at an unknown position is estimated fromthe position information of at least three known or position-estimatedtransmitting stations, and (B) the position of an unknown transmittingstation is estimated from the position information of at least threeknown and/or position-estimated receiving stations. By repeatingoperations (A) and (B), the coordinates of unknown transmitting stationsare successively estimated.

[0296] As an application of the fourth embodiment, the fixed-positionreceiving station 51 a can be realized as a gate, and the movingreceiving station 51 b can be attached to an object, such as a vacuumcleaner, that travels around within a predetermined area.

[0297] Although in the fourth embodiment only a single fixed-positionreceiving station is used, two or more fixed-position receiving stationsmay be combined with a moving receiving station. In this case, if thenumber of fixed-position receiving stations is rn, and if the number ofknown transmitting stations is tn, then rn×tn≧rn+4 and rn×tn≧rn+2 mustbe satisfied. If two fixed-position receiving stations are used, thenumber of know transmitting stations required at the initial stage istwo.

[0298] [Fifth Embodiment]

[0299]FIG. 30 illustrates a locating system according to the fifthembodiment, and FIG. 31 illustrates the structures of the transmittingstation 21 and the receiving station 51 used in the system shown in FIG.30. In the fifth embodiment, a single moving receiving station is solelyused, without using a fixed-position receiving station.

[0300] As illustrated in FIG. 30, the locating system of the fifthembodiment comprises a moving receiving station 51, transmittingstations 21 (T1-T10), a server 12, a positioning computer 11, and userterminal 3. The positioning computer 11, the server 12, and the userterminals are mutually connected via LAN 2. Since, in the fifthembodiment, a single moving receiving station 51 is used, the server 12has a wireless LAN base station 41, and the receiving station 51 has awireless LAN cellular station 40.

[0301] The moving receiving station 51 has a microcontroller 32, areceiver 33, a transmitter 34, an activation signal generator 35, ananti-collision determination unit 36, and a time computation unit 37.The microcontroller 32 controls the operation of the receiving station51 and has built-in memories, such as ROM and RAM. The activation signalgenerator 35 generates an activation signal, and the transmitter 34transmits the activation signal to transmitting stations. The receiver33 receives an ID signal from each transmitting station and measures theintensity of the received ID signal. The anti-collision determinationunit 36 reads or extracts the identifier from the ID signal. The timecomputation unit 37 measures a transmission time required to acquire theID signal. In the fourth embodiment, transmission time is the timerequired to read the identifier since the generation of the activationsignal. However, the time computation unit 37 may be connected betweenthe transmitter 34 and the receiver 33. In this case, the transmissiontime is the time required to receive the ID signal since transmission ofthe activation signal.

[0302] The transmitting station 21 has the same structure as illustratedin the second through fourth embodiments. Namely, the transmittingstation 21 has a microcontroller 22, a transmitter 23, an ID signalgenerator 25, and a sensor 26. The ID signal generator 25 periodicallygenerates an ID signal containing a unique identifier (ID) of thattransmitting station 21. The microcontroller 22 controls the operationof the transmitting station 21, and has built-in memories, such as ROMand RAM. The receiver 24 receives the activation signal transmitted fromthe receiving station and supplies the activation signal to the IDsignal generator 25. The sensor 26 detects changes in variousparameters, which are caused by external factors 27, and supplies thedetection result to the ID signal generator 25. The ID signal generator25 generates different kinds of ID signals when receiving the activationsignal from the receiving station and when detecting a change, inaddition to a periodic signal of a relatively long interval. With thisarrangement, an ID signal is transmitted when it is actually required,and power consumption of the battery can be reduced. The size of the logfile can also be reduced. The sensor 26 is realized by combining anacceleration sensor using an inverted pendulum, a light sensor, atemperature sensor, a humidity sensor, and other types of sensors.

[0303] The positioning computer 11 estimates the position of atransmitting station based on the data supplied from the single movingreceiving station 51 via the wireless LAN to the server 12, according tothe algorithm described below.

[0304] <Algorithm for Correcting Transmission Time>

[0305] In the example shown in FIG. 30, the positions of transmittingstations T1-T7 are known (and these transmitting stations are referredto as “known transmitting stations”). The moving receiving station 51travels with its position changing R1→R2→R3→R4, as indicated by thedashed arrows. The initial position R1 of the moving receiving station51 is (u1, v1), and the j^(th) position of the moving receiving station51 is (uj , vj) The positions of transmitting stations T8-T10 areunknown (and these transmitting stations are referred to as “unknowntransmitting stations”), and the position of the i^(th) transmittingstation is (xi, yi). An ID signal is transmitted from a transmittingstation to the receiving station 51 via electromagnetic waves, and theintensity of the ID signal received at the receiving station at thej^(th) position (referred to as the j^(th) receiving station forconvenience) is e_(ij). The distance between the i^(th) transmittingstation and the j^(th) receiving station is d_(ij), which is expressedby Equation (1).

d _(ij)={square root}{square root over ((x_(i) −u _(j))²+(y_(i) −v_(j))²)}  (1)

[0306] First, transmission time t_(ij), required to acquire the IDsignal and read the identifier, is corrected using known positioninformation of the known transmitting stations. The transmission timet_(ij) is the sum of a propagation time p_(ij) of the signal(electromagnetic wave in this embodiment) through the air, a signalpropagation time A in the receiving station, and a signal propagationtime b in the transmitting station.

t _(ij) =p _(ij) +A+b  (6)

[0307] Among the terms in the right-hand side, propagation time A in thereceiving station 51 can be regarded as constant because a high-speedreceiving operation is realized using a sufficient power source. Incontrast, the propagation time b in the transmitting station 21 has astrong correlation with the intensity e_(ij) because of thereversibility of propagation depending on the configuration of theactivation signal detection circuit (not shown) of each transmittingstation. The correlation varies depending on the technique for detectingthe activation signal, and an approximate formula using a polynomial oran exponential function can be applied. For example, receipt of theactivation signal is sensed by a diode, charging a capacitor. Then, itcan be regarded that the activation signal has been detected when thevoltage reaches a predetermined level. In this case, an approximateformula defined by Equation (7) is assumed using an exponentialfunction, which describes the correlation between intensity e_(ij) andpropagation time b in the transmitting station.

b=f+g exp(−h×e _(ij))  (7)

[0308] In Equation (7), f, g, and h are correcting coefficients.Equation (7) is inserted in Equation (6) to obtain Equation (8).

t _(ij) =p _(ij) +A+f+g exp(−h×e _(ij))  (8)

[0309] Since distance d_(ij) between the transmitting station 21 and thereceiving station 51 is proportional to signal propagation time p_(ij)through the air, Equation (8) is modified as Equation (19).

p _(ij) =t _(ij) −A−f−g exp(−h×e _(ij))=Kd _(ij) =K{square root}{squareroot over ((x _(i) −u _(j))²+(y _(i) −v _(j))²)}  (19)

[0310] where K is a proportional constant.

[0311] At this stage, e_(ij) is the intensity of the ID signaltransmitted from each of transmitting stations T1-T7 whose positions arealready known (referred to as “known transmitting stations”). Unknownparameters are seven, that is, A, F, g, h, K, uj and vj. If A and f areconsidered as a single parameter B (=A+f), then the number of unknownsbecomes six. The solutions for these unknowns that minimize the errorare obtained by minimizing estimation function qqqq expressed byEquation (20). $\begin{matrix}{{qqqq} = {\sum\limits_{j = 1}^{rn}\quad {\sum\limits_{i = 1}^{tn}\quad ( {t_{ij} - \overset{\Cap}{B} - {\overset{\Cap}{g}\quad {\exp ( {{- \overset{\Cap}{h}} \times e_{ij}} )}} - {\overset{\Cap}{K}\sqrt{( {x_{i} - {\overset{\Cap}{u}}_{j}} )^{2} + ( {y_{i} - {\overset{\Cap}{v}}_{j}} )^{2}}}} )^{2}}}} & (20)\end{matrix}$

[0312] where rn is the number of the receiving stations, and tn is thenumber of known transmitting stations. In order to solve all theunknowns, rn×tn≧3×rn+4 must be satisfied. In the example shown in FIG.30, rn is one and tn is seven, and therefore, all the unknowns can besolved. For the purpose of clarification, unknowns are marked with anarc above the symbols.

[0313] There are many known methods for solving Equation (20). Forexample, partially differentiating function qqqq with respect to eachvariable, and obtaining the numerical solutions that make the respectivepartial differentials zero using, for example, the Newton method.Alternatively, the simplex method, the steepest descent method (orsaddle point method), methods using neural networks can be used. Usingany one of these methods, the correcting coefficients B, g and h, aproportional constant K for the signal propagation time p_(ij) anddistance d_(ij), and the position (uj, vj) of the receiving station 51are determined.

[0314] Distance nnd_(ij) from an unknown transmitting station to a knownreceiving station can be derived using the signal propagation timep_(ij) determined by Equation (20). The relation between nd_(ij) andp_(ij) is expressed by Equation (21) using proportional constant K.$\begin{matrix}{{nnnd}_{ij} = {\frac{p_{ij}}{K} = \frac{\{ {t_{ij} - B - {g\quad {\exp ( {{- h} \times e_{ij}} )}}} \}}{K}}} & (21)\end{matrix}$

[0315] where nnd_(ij) is a distance derived from the measuredtransmission time. Then, the position of an unknown transmitting stationcan be estimated using K, B, g, h determined by Equation (20) incombination with the intensity and the transmission time measured at theposition-estimated receiving station 51.

[0316] <Algorithm Used When the Moving Receiving Station Travels>

[0317] As the moving receiving station 51 travels from R1 to R2, and toR3, the new position (uj, vj) of the moving receiving station 51 can beestimated using position information of the known transmitting stationsT1-T7, using Equation (20).

[0318] The moving receiving station 51 transmits an activation signal toan unknown transmitting station at each of the estimated positions.Then, at least three estimated positions “j” of the receiving station 51are used to estimate the position (xi, yi) of the unknown transmittingstation “i”. The estimation is made by minimizing estimation functionhhhhhhhi expressed by Equation (22). $\begin{matrix}{{hhhhhh}_{\quad i} = {\sum\limits_{j = 1}^{rrrn}\quad ( {\frac{\{ {t_{ij} - B - {g\quad {\exp ( {{- h} \times e_{ij}} )}}} \}}{K} - \sqrt{( {{\overset{\Cap}{x}}_{i} - u_{j}} )^{2} + ( {{\overset{\Cap}{y}}_{i} - v_{j}} )^{2}}} )^{2}}} & (22)\end{matrix}$

[0319] where rrrn is the number of available (estimated) positions ofthe moving receiving station 51. For the purpose of clarification, theunknowns are marked with an arc above the symbols.

[0320] <Algorithm Used When Known Transmitting Station is Out of Area>

[0321] As the moving receiving station 51 travels, the transmittingstations T1-T7 fixed at known positions are out of the communicationarea of the receiving station 51. Accordingly, the positions oftransmitting stations T8-T10, which have already been estimated in theabove-described manner, are used to estimate a new position of themoving receiving station 51.

[0322] The positions of transmitting stations T8-T10 are successivelyestimated using the time-correcting algorithm using the secondcorrecting formula and the algorithm for a moving receiving station. Bymaking use of the estimated position information, the estimationaccuracy for the environmental coefficient Kti for the transmittingstation can be improved.

[0323] As in the previous embodiments, environmental coefficient Krj forthe receiving station “j” is first defined. The environmentalcoefficient Krj is an index indicating how the sensitivity of thereceiving station changes from the ideal condition. Similarly,environmental coefficient Kti for a target transmitting station is alsodefined.

[0324] First, the Friis' formula is corrected using correctingcoefficients S1, S2, and an environmental coefficient Krj to define arelation between distance “d” and intensity “e”, using the actuallymeasured values between the transmitting station 21 and the receivingstation 51. Based on the assumption that distance and intensity are inthe logarithmic relation, Equation (2) is defined.

e _(ij) =S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)

[0325] where S1 and S2 are correcting coefficients. At this stage,e_(ij) is the intensity of the ID signal transmitted from each of theknown transmitting stations T1-T7. The solutions for the unknownparameters that make the error minimum are obtained by minimizingestimation function q expressed by Equation (3). $\begin{matrix}{q = {\sum\limits_{j = 1}^{rn}\quad {\sum\limits_{i = 1}^{tn}\quad ( {e_{ij} - {{\overset{\Cap}{S}}_{1}{\log_{10}( d_{ij} )}} - {\overset{\Cap}{S}}_{2} + {\overset{\Cap}{K}}_{rj}} )^{2}}}} & (3)\end{matrix}$

[0326] where rn is the number of receiving stations whose positions areknown, and tn is the number of known transmitting stations. To solve allthe unknowns, un×tn≧rn+2 must be satisfied. In the example shown in FIG.26, rn is one and tn is seven, and therefore, all the unknowns aresolved. For clarification, unknowns are marked with an arc above thesymbols.

[0327] There are many methods for solving Equation (3), for example, bypartially differentiating function q with respect to each variable andobtaining the numerical solutions that make the respective partialdifferentials zero using the Newton method. Alternatively, the simplexmethod, the steepest descent method (or saddle point method), methodsusing neural networks can be used. Using any one of these methods, thecorrecting coefficients S1, S2 and environmental coefficient Krj aredetermined.

[0328] Next, environmental coefficient Kti for an unknown transmittingstation is introduced. Although the transmitting intensity at atransmitting station is constant, the environmental coefficient variesdepending on the location, and therefore, a relation between intensityand distance is assumed as Equation (4) introducing environmentalcoefficient Kti for transmitting station. Equation (4) contains thecoefficients S1, S2 and the environmental coefficient Krj for thereceiving station that have been determined by Equation (3).$\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj} + K_{ti}})}/S_{1}}} & (4)\end{matrix}$

[0329] where md_(ij) is a distance derived from the measured intensity.Kti can be determined by minimizing the estimation function hhhhhhhiexpressed by Equation (23). $\begin{matrix}{{hhhhhhhh}_{\quad i} = {\sum\limits_{j = 1}^{rn}\quad ( {10^{{({e_{ij} - S_{2} + K_{rj} + {\overset{\Cap}{K}}_{ti}})}/S_{1}} - \sqrt{( {x_{i} - u_{j}} )^{2} + ( {y_{i} - v_{j}} )^{2}}} )^{2}}} & (23)\end{matrix}$

[0330] For clarification, unknowns are marked with an arc above thesymbols. In Equation (23), position (xi, yi) is described usingestimated values which are determined from the measured intensity andtransmission time using Equation (22).

[0331] As in the first through fourth embodiments, when an ID signalcannot be received at a certain receiving station, this unknowninformation is made use of as a restrictive condition. For example, asignal from transmitting station T2 is received at positions R1, R2, andR3 of the receiving station, but is not received at R4. In this case,restrictive conditions

[0332] d21<d24

[0333] d22<d24

[0334] d23<d24

[0335] are added. Thus, even unknown information is not discarded, andinstead, it is effectively used in position estimation.

[0336]FIG. 32 illustrates the operation flow of the positioning computer11 according to the fourth embodiment. The positioning computer 11checks time stamps of data stored in the server 12 and determineswhether a predetermined amount of time has passed (S531). This step iscarried out in order to prevent overlooking because the transmittingstation operates discontinuously and because the ID signals may not bereceived due to signal overlap. If a predetermined time has passed (YESin S531), then the current data are compared with the previous data foreach identifier (S532) to determine if the current data have beenupdated (S533). If there are data elements updated from the previousones (YES in S533), data of fixed-position transmitting stations (T1-T7in example shown in FIG. 30) whose positions are known in advance areextracted from all the updated data. Using the data of thefixed-position transmitting stations, correcting coefficients B, g, hand proportional constant K for ratio of p_(ij) (signal propagation timethrough the air) to d (distance) that minimize Equation (20) aredetermined. In addition, correcting coefficients S1, S2 andenvironmental coefficient Krj that minimize Equation (3) are determinedto provide a propagation formula for the electromagnetic field (S534).

[0337] (A) Then, data of known or position-estimated transmittingstations are extracted from the data supplied from the moving receivingstation 51 at an unknown position (S535). It is then determined whetherthe ID signal from a data-updated transmitting station is of type a(S536). If the ID signal is of type a (YES in S536), Equation (20) issolved using the measured intensity and transmission time to estimatethe position of the moving receiving station. The estimation result isstored in the server 12. Furthermore, Equation (3) is solved todetermine the environmental coefficient Krj of the moving receivingstation at the estimated position, which is also stored in the server 12(S537).

[0338] On the other hand, if the ID signal is one of types b-f (NO inS536), there is no information about the transmission time, andtherefore, Equation (3) is solved, with the position of the movingreceiving station as an unknown parameter, to estimate the position andthe environmental coefficient of the receiving station The estimationresult is stored in the server 12 (S538).

[0339] (B) Then, data of an unknown transmitting station is extractedfrom the data supplied from the moving receiving station 51 at theestimated positions (S539). It is determined as to the data-updatedtransmitting station whether the ID signal is of type a (S540). If theID signal is of type a (YES in S540), Equation (22) is solved using themeasured transmission time and intensity to estimate the position of theunknown transmitting station, which is stored in the server 12.Furthermore, Equation (23) is solved to estimate the environmentalcoefficient Kti for that transmitting station, which is also stored inthe server 12. (S541).

[0340] On the other hand, if the ID signal is not of type a (NO inS540), then Equation (23) is solved, with the position of the targettransmitting station as an unknown parameter, to estimate the positionand the environmental coefficient of the target (unknown) transmittingstation. The estimation result is stored in the server 12 (S542).

[0341] Algorithms (A) and (B) are repeated for all the data-updatedtransmitting stations (YES in S543). When all the updated data have beenprocessed (NO in S543), the current estimation result is compared withthe previous one to select those transmitting stations that have moved apredetermined amount or more (YES in S544) and those transmittingstations from which ID signals are not received at any receivingstations (YES in S545). The selection result is stored in the server 12(S546), and an alert message is supplied to the associated user terminal(S547).

[0342] Table 9 shows an example of a data structure recording the datafrom the receiving station 51 in the server 12, and Table 10 shows anexample of a data structure recording the estimation result suppliedfrom the positioning computer 11. TABLE 9 DATA STRUCTURE OF SIGNALINFORMATION SUPPLIED FROM RECEIVING STATION RS ID TS ID ID TYPE TIMESTAMP TRANSMISSION TIME INTENSITY 0001 0015 a 16:33:10 00:00:00000080 240001 0015 c 17:33:10 23 0002 0015 a 16:33:40 00:00:00000050 14 0002 0016a 16:33:40 00:00:00000061 13 0002 0017 a 16:33:10 00:00:00000070 12 00020018 a 16:33:10 00:00:00000075 14

[0343] TABLE 10 DATA STRUCTURE OF ESTIMATION RESULTS SUPPLIED FROMPOSITIONING COMPUTER TS ID ID TYPE TIME STAMP ESTIMATION (X, Y) ENVIR'LCOEFF. 0015 a 17:22:21 11.34, 9.15 31.0 0015 c 18:22:21 11.95, 9.25 32.4RS ID ID TYPE TIME STAMP ESTIMATION (X, Y) ENVIR'L COEFF. 0002 a17:22:23  5.34, 3.15 10.0 0002 c 18:22:24  6.95, 4.25 12.4

[0344] Environmental coefficient Kti reflects the environmentsurrounding a transmitting station, and it provides useful informationwhen actually trying to determine the location of the transmittingstation. If the environmental coefficient is large, it indicates thatthe transmitting station is located at an obstructed place with respectto the receiving station. If the environmental coefficient is small, thetransmitting station is located at an open space or an unobstructedplace. Adding such environmental information to the estimated positionallows the user to actually locate the target transmitting station.

[0345] The user terminal 3 has two functions, as in the first throughfourth embodiments, that is receiving an alert message supplied from thepositioning computer 11, and retrieving the position of a targettransmitting station. The user inputs the identifier (ID) of the targettransmitting station into the user terminal. The user terminal accessesthe server 12 to retrieve in the server 12 the past record of thatidentifier, such as time stamps, position information, environmentalcoefficient, etc. The retrieved result is displayed on the userterminal.

[0346] The user can determine whether the target transmitting station islocated at an open space from the position information described by timestamps and the corresponding environmental coefficient. In addition, theuser can determine when an activation signal is received at thetransmitting station or when external change has been detected from thepast record.

[0347] In the fifth embodiment, accurate position estimation for a largenumber of transmitting stations is realized over a wide area, using asingle moving receiving station. Using a fixed-position receivingstation requires the number of receiving station to be increased, andthe cost for system construction increased. With the system of the fifthembodiment, the construction cost and the maintenance cost are greatlyreduced.

[0348] If the receiving station is moved in the conventional system, thepresence or absence can be confirmed, but the position coordinates cannot be obtained. In contrast, the locating system of the fifthembodiment can estimate the position of an unknown transmitting stationallowing the receiving station to travel around. That is, first andsecond correcting formulas are determined using position informationabout seven known transmitting station T1-T7. Then (A) the position ofthe moving receiving station is estimated using information about atleast known or position-estimated transmitting stations, and (B) theposition of an unknown transmitting station is estimated usinginformation about at least three estimated positions of the receivingstation. By repeating (A) and (B), position information of unknowntransmitting stations is successively acquired over a wide area.

[0349] By determining the environmental coefficient for a transmittingstation, position estimation becomes more accurate taking theenvironment into account.

[0350] As an application of the fifth embodiment, the moving receivingstation 51 is attached to an object, such as a vacuum cleaner, thattravels around within a predetermined area. As the object (or the vacuumcleaner) travels, the entire area can be checked regularly andautomatically. Inventories or assets are controlled over a wide areawithout using a large number of fixed-position receiving stations.Consequently, the cost of the entire system can be reduced, and aneconomical and efficient system can be achieved.

[0351] [Sixth Embodiment]

[0352] In the first through fifth embodiments, a first correctingformula expressed as

e _(ij) =S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)

[0353] is used when estimating the position of a transmitting station.In the sixth embodiment, a modification of the first correcting formula(Equation (2)) is provided. The modified formula will be explained usingthe locating system of the first embodiment shown in FIGS. 5 and 6.

[0354] There are four receiving stations R1-R4 whose positions are knownin advance. There are eight transmitting stations T1-T8, among which thepositions of T1-T4 are known. The position of the j^(th) known receivingstation is (uj, vj), and the position of the i^(th) transmitting stationis (xi, yi). The intensity of the ID signal received at the j^(th)receiving station is e^(ij), and the distance between the i^(th)transmitting station and the j^(th) receiving station is expressed byEquation (1).

d _(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j))²)}  (1)

[0355] Then, environmental coefficient Krj for the j^(th) receivingstation is defined. Environmental coefficient Krj is an index indicatinghow the sensitivity of the receiving station changes from the idealcondition. Similarly, environmental coefficient Kti for the i^(th)transmitting station is defined. The Friis' formula is corrected usingcorrecting coefficients S1, S2, and an environmental coefficient Krj todefine a relation between distance “d” and intensity “e”, on theassumption that distance and intensity are in the logarithmic relation.The corrected formula is expressed as

e _(ij) =S ₁×log₁₀(d _(ij) +S ₂)−K _(rj)  (24)

[0356] where S1, S2 are correcting coefficients, and e_(ij) is theintensity of the ID signal transmitted from the known transmittingstations T1-T4. The solutions for the unknown parameters that make theerror minimum are obtained by minimizing estimation function q expressedby Equation (25). $\begin{matrix}{q = {\sum\limits_{j = 1}^{rn}\quad {\sum\limits_{i = 1}^{tn}\quad ( {e_{ij} - {{\overset{\Cap}{S}}_{1}{\log_{10}( {d_{ij} + {\overset{\Cap}{S}}_{2}} )}} + {\overset{\Cap}{K}}_{rj}} )^{2}}}} & (25)\end{matrix}$

[0357] where rn is the number of receiving stations whose positions areknown, and tn is the number of known transmitting stations. To solve allthe unknowns, un×tn≧rn+2 must be satisfied. In the example of the firstembodiment, rn is four and tn is four, and therefore, all the unknownsare solved. For clarification, unknowns are marked with an arc above thesymbols.

[0358] There are many methods for solving Equation (25) for example, bypartially differentiating function q with respect to each variable andobtaining the numerical solutions that make the respective partialdifferentials zero using the Newton method. Alternatively, the simplexmethod, the steepest descent method (or saddle point method), methodsusing neural networks can be used. Using any one of these methods, thecorrecting coefficients S1, S2 and environmental coefficient Krj aredetermined.

[0359] Next, environmental coefficient Kti for a target transmittingstation whose position is unknown (simply referred to as “unknowntransmitting station”) will be introduced. Although the transmittingintensity at a transmitting station is constant, the environmentalcoefficient varies depending on the location, and therefore, theintensity of the received signal varies. Accordingly, a relation betweenintensity and distance is assumed as defined in Equation (26), using theenvironmental coefficient Krj, and correcting coefficients S1 and S2determined by Equation (25) $\begin{matrix}{{md}_{ij} = {10^{{({e_{ij} + K_{rj} + K_{ti}})}/{(S_{1})}} - S_{2}}} & (26)\end{matrix}$

[0360] where md_(ij) is a distance derived from the measured intensity,and Kti is environmental coefficient for the transmitting station “i”.The position and the environmental coefficient of the transmittingstation “i” are obtained by minimizing estimation function (27).$\begin{matrix}{h_{i} = {\sum\limits_{j = 1}^{rn}\quad ( {10^{{({e_{ij} + K_{rj} + {\overset{\Cap}{K}}_{tr}})}/{(S_{1})}} - S_{2} - \sqrt{( {{\overset{\Cap}{x}}_{i} - u_{j}} )^{2} + ( {{\overset{\Cap}{y}}_{i} - v_{j}} )^{2}}} )^{2}}} & (27)\end{matrix}$

[0361] In this manner, the position and the environmental coefficient ofan unknown transmitting station can be estimated accurately from theactually measured intensity and known position information, using amodified correcting formula.

[0362]FIG. 33 and FIG. 34 illustrate test results of actually estimatingpositions of transmitting stations using the locating system 1 shown inFIG. 5, using the modified first correcting formula. In the test, fourreceiving stations are fixed at positions indicated by pos1-pos4. FIG.33 shows the estimation result for transmitting station T6, and FIG. 34shows the estimation result for transmitting station T7. The circleindicates the actual position of the transmitting station, and the crossindicates the estimated position using the modified first correctingformula. The estimation function expressed by Equation (27) isincorporated as contour lines in the diagrams. The estimation error fortransmitting station T6 is 0.4 in the X-direction and 0.9 in theY-direction, and the corresponding distance is 1.0. The estimation errorfor transmitting station T7 is 0.9 in the X-direction and −0.7 in theY-direction, and the corresponding distance is 1.14. The square in thediagram is a unit area on the floor, and a side is 1.35 m.

[0363] The conventional systems have only a function of specifyingpresence or absence of a transmitting station within the communicationarea of a certain receiving station. For this reason, the positionestimated by the conventional systems agrees with the position of thereceiving station that has the maximum intensity. With the conventionalsystem, the estimated position of the transmitting station agrees withthe position of pos2 in FIG. 33, and the estimation error is −6.0 in theX-direction and −5.0 in the Y-direction. The corresponding distance is7.8. In the example of FIG. 34, the position estimated by theconventional system agrees with pos4, and the estimation error is 3.0 inthe X-direction and 3.0 in the Y-direction. The corresponding distanceis 4.3. Comparing these results with the estimation results of the sixthembodiment, the estimation accuracy of the sixth embodiment is 8 timesas high as the conventional system for transmitting station T6, and fourtimes as high as the conventional system for transmitting station T7.

[0364] In the test, the transmitting station T6 is located at an openspace, while the transmitting station T7 is placed in a steal box. Theenvironmental coefficients Kt6 and Kt7 determined by the locating systemusing the above-described algorithm are −2.99 and 16.01, respectively,which are consistent with the actual environment. This fact proves thatenvironmental coefficients provide effective information for positionestimation.

[0365] In the above-described example, a modification of the correctedFriis' formula (i.e., the first correcting formula) is expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)−K _(rj)  (24)

[0366] However, only correcting coefficients S1 and S2 may be usedwithout environmental coefficient. In this case, the correcting formulais expressed as

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)  (24)′

[0367] In addition, the correcting formula expressed by Equation (24)′or (24)″ may be used for a transmitting station.

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)−K _(rj)  (24)″

[0368] The sixth embodiment has been described using an example in whichEquation (24) is used for a receiving station and Equation (24)″ is usedfor a transmitting station. However, Equation (24)′ may be used for bothtransmitting stations and receiving stations. In this case, the positionof an unknown transmitting station is estimated still with highprecision. If using Equation (24)′, estimation function (27)′ isdetermined using Equation (26)′. $\begin{matrix}{{md}_{ij} = {10^{{(e_{ij})}/{(S_{1})}} - S_{2}}} & (26)^{\prime}\end{matrix}$

$\begin{matrix}{h_{ij} = {\sum( {10^{{(e_{ij})}/{(S_{1})}} - S_{2} - d_{ij}} )^{2}}} & (27)^{\prime}\end{matrix}$

[0369] If Equation (24)′ is used for a receiving station and Equation(24)″ is used for a transmitting station, then estimation function ofEquation (27)″ is determined using Equation (26)″. $\begin{matrix}{{md}_{ij} = {10^{{({e_{ij} + K_{ti}})}/{(S_{1})}} - S_{2}}} & (26)^{''} \\{h_{ij} = {\sum( {10^{{({e_{ij} + K_{ti}})}/{(S_{1})}} - S_{2} - d_{ij}} )^{2}}} & (27)^{''}\end{matrix}$

[0370] If Equation (24) is used for a receiving station and Equation(24)′ is used for a transmitting station, estimation function ofEquation (27)′″ is determined using Equation (26)′″. $\begin{matrix}{{md}_{ij} = {10^{{({e_{ij} + K_{rj}})}/{(S_{1})}} - S_{2}}} & (26)^{\prime\prime\prime} \\{h_{ij} = {\sum( {10^{{({e_{ij} + K_{rj}})}/{(S_{1})}} - S_{2} - d_{ij}} )^{2}}} & (27)^{\prime\prime\prime}\end{matrix}$

[0371] It is needless to say that the modified correcting formulasexplained in the sixth embodiment can be used not only in the locatingsystem of the first embodiment, but also in the locating systems of thesecond through fifth embodiments.

[0372] [Other Embodiments]

[0373] Although the invention has been described based on the preferredembodiments, the invention is not limited to these examples, but coversmany modifications, changes, and substitutions within the capabilitiesof a person skilled in the art, without departing from the scope of theinvention. For example, the object (or the target) of positionestimation is not limited to a transmitting station as a tag, and theposition of an arbitrary item that can transmit a signal can beestimated. The transmitting station may have both transmitting andreceiving functions, like a cellular phone or a mobile terminal. In thiscase, the location of a person who has such a device can be estimatedand managed. In addition, both the transmitting station and thereceiving station may have transmitting/receiving functions.

[0374] In the second through fifth embodiments, the activation signal isgenerated and supplied by the receiving station in order to cause atransmitting station to transmit an ID signal. However, the activationsignal may be supplied from a high-powered remote base station bymulticasting. In this case, the system can obtain data or informationabout a large number of transmitting stations through remote operations.This arrangement can reduce manpower and improve data-collectingefficiency. Besides, the structure of the receiving station can besimplified.

[0375] The receiving station may be connected to the server (or the datamanagement unit) via cable or in a wireless manner. If using a movingreceiving station as in the fourth and fifth embodiments, it ispreferable to use wireless network, such as wireless LAN. In this case,a single system can control the assets or entire inventory over multiplefloors or buildings. The user terminal may also be connected to theserver via a cable or a wireless network. In either case, the usersimply inputs the identifier (or identification number) of a tagattached to an item to have the positioning computer estimate theposition of that item.

[0376] In the first through fifth embodiments, a first correctingformula expressed as

e _(ij) =S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)

[0377] is used for a receiving station. However, only the correctingcoefficients S1 and S2 may be used in the formula without using theenvironmental coefficient Krj. In this case, the first correctingformula for a receiving station is expressed by Equation (2)

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂  (2)′

[0378] Similarly, for a transmitting station, Equation (2)′ or (2)″ maybe used as a first correcting formula.

e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂ −K _(rj)  (2)″

[0379] If Equation (2)′ is used for both transmitting station andreceiving station, Equations (4)′ and (5)′ are used in place of Equation(4) and (5) to express a derived distance and an estimation function,respectively. $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2}})}/S_{1}}} & (4)^{\prime} \\{h_{ij} = {\Sigma ( {10^{{({e_{ij} - S_{2}})}/S_{1}} - d_{ij}} )}^{2}} & (5)^{\prime}\end{matrix}$

[0380] If Equation (2)′ is used for a receiving station and Equation(2)″ is used for transmitting station, then an estimation functionexpressed by Equation (5)″ is solved using Equation (4)″ to determinethe position. $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{ti}})}/S_{1}}} & (4)^{''} \\{h_{ij} = {\Sigma ( {10^{{({e_{ij} - S_{2} + K_{ti}})}/S_{1}} - d_{ij}} )}^{2}} & (5)^{''}\end{matrix}$

[0381] If Equation (2) is used for a receiving station and Equation (2)′is used for a transmitting station, then an estimation functionexpressed by Equation (5)′″ is solved using Equation (4)′″ to determinethe position. $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj}})}/S_{1}}} & (4)^{\prime\prime\prime} \\{h_{ij} = {\Sigma ( {10^{{({e_{ij} - S_{2} + K_{rj}})}/S_{1}} - d_{ij}} )}^{2}} & (5)^{\prime\prime\prime}\end{matrix}$

[0382] If Equation (2)′ using only S1 and S2 is selected as a firstcorrecting formula, and if there is no known transmitting station(tn=0), then the number of known receiving stations must satisfy rn≧5.Similarly, if there is no known receiving station (rn=0), the number ofknown transmitting station must satisfy tn≧5.

[0383] If Equation (2)″ using environmental coefficient Kti is selectedas a first correcting formula, and if there is no known transmittingstation (tn=0), then the number of known receiving station must satisfyrn≧6. Similarly, if there is no known receiving station (rn=0), thenumber of known transmitting station must satisfy tn≧6.

[0384] The fourth and fifth embodiments are explained using an examplein which the number of known transmitting stations is greater than thenumber of known positions of the receiving station in the initial state.Accordingly, after the unknown parameters of the correcting formulas aredetermined, an algorithm of estimating the position of the receivingstation, then estimating the position of an unknown transmitting stationusing the estimated position of the receiving station, and then furtherestimating the new position of the receiving station is repeated.However, the number of known positions of the receiving station may begreater than the number of known transmitting stations in the initialstate. In this case, after the correcting formula(s) is/are determined,an algorithm of estimating the position of a transmitting station, thenestimating the new position of the receiving station, and furtherestimating the position of another transmitting station is repeated.

[0385] In the former case (of first estimating the position of thereceiving station),

[0386] (a) a first approximate function

e _(ij) =f ₀(d _(ij))=f ₀({square root}{square root over ((u _(i) −x_(j))²+(v _(i) −y _(j))²)})

[0387] is determined as a first correcting formula, using a firstintensity e_(ij) of a first signal transmitted from at least one knowntransmitting station “i” located at a known position (ui,vi) andmeasured at a receiving station “j” located at a first unknown position(xj,yj), as well as a distance d_(ij) from the transmitting station “i”to the receiving station “j”, to derive a position (uj, vj) of the firstunknown position of the receiving station “j”;

[0388] (b) a second approximate function

e _(ij) =f ₀({square root}{square root over ((x _(i) −u _(j))²+(y _(i)−v _(j))²)})

[0389] is defined based on the first correcting formula, using a secondintensity e_(ij) of a second signal transmitted from an unknowntransmitting station “i” located at an unknown position (xi, yi) andmeasured at a known or position-estimated receiving station “j”, as wellas position information (uj, vj) of said known or position-estimatedreceiving station “j”, to derive a position (ui, vi) of said unknowntransmitting station “i”; and then

[0390] (c) a third approximate function

e _(ij) =f ₀({square root}{square root over ((u _(i) −x _(j))²+(v _(i)−y _(j) ²)})

[0391] is defined based on the first correcting formula, using a thirdintensity e_(ij) of a third signal transmitted from a known orposition-estimated transmitting station “i” located at (ui,vi) andmeasured at the receiving station “j” at a second unknown position, aswell as position information of said known or position-estimatedtransmitting station “i”, to derive a position (uj, vj) of the secondunknown position of the receiving station “j”. The steps (b) and (c) arerepeated to successively estimate positions of an unknown receivingstation and an unknown transmitting station.

[0392] In the latter case (of first estimating the position of atransmitting station),

[0393] (a) a first approximate function

e _(ij) =f ₀(d _(ij))=f ₀({square root}{square root over ((x _(i) −u_(j))²+(y _(i) −v _(j))²)})

[0394] is determined as a first correcting formula, using a firstintensity e_(ij) of a first signal transmitted from a first unknowntransmitting station “i” located at a first known position (xi,yi) andmeasured at one or more known receiving stations “j” located at knownpositions (uj,vj), as well as a distance d_(ij) from the transmittingstation “i” to the receiving station “j”, to derive a position (ui, vi)of the first unknown transmitting station “i”;

[0395] (b) a second approximate function

e _(ij) =f ₀({square root}{square root over ((u _(i) −x _(j))²+(v _(i)−y _(j))²)})

[0396] is defined based on the first correcting formula, using a secondintensity e_(ij) of a second signal transmitted from a known orposition-estimated transmitting station “i” located at (ui, vi) andmeasured at an unknown receiving station “j” located at an unknownposition (xj, yj), as well as position information (ui, vi) of saidknown or position-estimated transmitting station “i”, to derive aposition (uj, vj) of said unknown receiving station “j”; and then

[0397] (c) a third approximate function

e _(ij) =f ₀({square root}{square root over ((x _(i) −u _(j))²+(y _(i)−v _(j))²)})

[0398] is defined based on the first correcting formula, using a thirdintensity e_(ij) of a third signal transmitted from a second unknowntransmitting station “i” located at a second unknown position (xi,yi)and measured at a known or position-estimated receiving station “j” at(uj, vj), as well as position information of said known orposition-estimated receiving station “j”, to derive a position (ui, vi)of the second unknown position of the second unknown transmittingstation “i”, the steps (b) and (c) being repeated to successivelyestimate positions of an unknown transmitting station and an unknownreceiving station.

[0399] The same applies to the algorithm using the second correctingformula. Although in the fourth and fifth embodiments the position ofthe moving receiving station is first estimated after the unknownparameters of the second correcting formula are determined; the positionof an unknown transmitting station may be first estimated if there aremany known or estimated positions of the receiving station.

[0400] In the former case (of estimating the position of the movingstation first),

[0401] (a) a first approximate function

p _(i,j) =f ₁(t _(ij) ,e _(ij))=Kd _(ij) =K{square root}{square rootover ((u _(i) −x _(j))²+(v _(i) −y _(j))²)}

[0402] and a constant K are determined as a second correcting formula,using a first intensity e_(ij) of a first signal transmitted from atleast one known transmitting station “i” located at a known position(ui,vi) and measured at a receiving station “j” located at a firstunknown position (xj,yj), as well as a first signal transmission timetij, a first signal propagation time pij through the air, and positioninformation of said known transmitting station, to derive a position(uj, vj) of the first unknown position of the receiving station “j”;

[0403] (b) a second approximate function

f ₁(t _(ij) ,e _(ij))=K{square root}{square root over ((x _(i) −u_(j))²+(y _(i) −v _(j))²)}

[0404] is defined based on the second correcting formula, using a secondintensity e_(ij) of a second signal transmitted from an unknowntransmitting station “i” located at an unknown position (xi, yi) andmeasured at a known or position-estimated receiving station “j”, as wellas a second signal transmission time (tij) and position information (uj,vj) of said known or position-estimated receiving station “j”, to derivea position (ui, vi) of said unknown transmitting station “i”; and then

[0405] (c) a third approximate function

f ₁(t _(ij) ,e _(ij))K{square root}{square root over ((u _(i) −x_(j))²+(v _(i) −y _(j))²)}

[0406] is defined based on the second correcting formula, using a thirdintensity e_(ij) of a third signal transmitted from a known orposition-estimated transmitting station “i” located at (ui,vi) andmeasured at the receiving station “j” at a second unknown position, aswell as a third signal transmission time (tij) and position informationof said known or position-estimated transmitting station “i”, to derivea position (uj, vj) of the second unknown position of the receivingstation “j”. The steps (b) and (c) are repeated to successively estimatepositions of an unknown receiving station and an unknown transmittingstation.

[0407] In the latter case (of estimating the position of an unknowntransmitting station first),

[0408] (a) a first approximate function

p _(ij) =f ₁(t _(ij) ,e _(ij))=Kd _(ij) =K){square root}{square rootover ((x _(i) −u _(j))²+(y _(i) −v _(j))²)}

[0409] and constant K are determined as a second correcting formula,using a first intensity e_(ij) of a first signal transmitted from afirst unknown transmitting station “i” located at a first known position(xi,yi) and measured at one or more known receiving stations “j” locatedat known positions (uj,vj), as well as a first signal transmission time(tij), a first signal propagation time (pij) through the air, andposition information of said known receiving station “j”, to derive aposition (ui, vi) of the first unknown transmitting station “i”;

[0410] (b) a second approximate function

f ₁(t _(ij) ,e _(ij))=K{square root}{square root over ((u _(i) −x_(j))²+(v _(i) −y _(j))²)}

[0411] is defined based on the second correcting formula, using a secondintensity e_(ij) of a second signal transmitted from a known orposition-estimated transmitting station “i” located at (ui, vi) andmeasured at an unknown receiving station “j” located at an unknownposition (xj, yj), as well as a second signal transmission time (tij)and position information (ui, vi) of said known or position-estimatedtransmitting station “i”, to derive a position (uj, vj) of said unknownreceiving station “j”; and then

[0412] (c) a third approximate function

f ₁(t _(ij) ,e _(ij))=K{square root}{square root over ((x _(i) −u_(j))²+(y _(i) −v _(j))²)}

[0413] is defined based on the second correcting formula, using a thirdintensity e_(ij) of a third signal transmitted from a second unknowntransmitting station “i” located at a second unknown position (xi,yi)and measured at a known or position-estimated receiving station “j” at(uj, vj), as well as a third signal transmission time (tij) and positioninformation of said known or position-estimated receiving station “j”,to derive a position (ui, vi) of the second unknown position of thesecond unknown transmitting station “i”. The steps (b) and (c) arerepeated to successively estimate positions of an unknown transmittingstation and an unknown receiving station.

What is claimed is
 1. A system for determining a position of an object,comprising: a transmitting station configured to transmit a first IDsignal containing a first identifier in a periodic manner; a receivingstation configured to receive the first ID signal, measure an intensityof the first ID signal, and extract the first identifier; a datamanagement unit configured to store and manage the intensity inassociation with the first identifier; and a positioning computerconfigured to estimate a position of the transmitting station usinginformation stored in the data management unit.
 2. The system accordingto claim 1, wherein the receiving station comprises: an activationsignal generator configured to generate an activation signal for causingthe transmitting station to generate a second ID signal; and atransmitter configured to transmit the activation signal to thetransmitting station, and wherein the receiving station has an ID signalgenerator configured to generate the second ID signal containing asecond identifier in response to the activation signal.
 3. The systemaccording to claim 1, wherein the transmitting station receives anactivation signal supplied from a remote base station, and has an IDsignal generator configured to generate a second ID signal containing asecond identifier in response to the activation signal.
 4. The systemaccording to claim 1, wherein the transmitting station has a sensor forsensing a change due to an external factor, and an ID signal generatorconfigured to generate a third ID signal containing a third identifierwhen sensing the change.
 5. The system according to claim 4, wherein theID signal generator generates different types of said third identifiersdepending on types of changes.
 6. The system according to claim 1,wherein the positioning computer determines a first correcting formuladefining a relation between the intensity measured at the receivingstation and a distance between the transmitting station and thereceiving station, and estimates a position of an unknown transmittingstation using the first correcting formula and known positioninformation.
 7. The system according to claim 6, wherein the firstcorrecting formula is e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂ or e_(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂) where e_(ij) is theintensity of a signal transmitted from an i^(th) transmitting station at(xi,yi) and measured at a j^(th) receiving station at (uj, vj), d_(ij)is the distance from the i^(th) transmitting station to the j^(th)receiving station expressed as d _(ij)={square root}{square root over((x _(i) −u _(j))²+(y _(i) −v _(j))²)} and S1 and S2 are correctingcoefficients, wherein the positioning computer determines the correctingcoefficients S1 and S2 using the known position information to estimatethe position of the unknown transmitting station.
 8. The systemaccording to claim 7, wherein when using e _(ij) =f ₀(d _(ij))=S₁×log₁₀(d _(ij))+S ₂ as the first correcting formula, the positioningcomputer derives a distance md_(ij) = 10^((e_(ij) − S₂)/S₁)

from the measured intensity, and determines an estimation function${h_{ij} = {\sum\limits_{j = 1}^{rn}\quad ( {10^{{({e_{ij} - S_{2}})}/S_{1}} - d_{ij}} )^{2}}},$

and when using e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂) as thefirst correcting formula, the positioning computer derives a distancemd_(ij) = 10^((e_(ij))/(S₁)) − S₂

from the measured intensity, and determines an estimation functionh_(ij) = ∑(10^((e_(ij))/(S₁)) − S₂ − d_(ij))²

to weight with h_(ij)/md_(ij) to estimate the position of the unknowntransmitting station.
 9. The system according to claim 6 wherein thefirst correcting formula is e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂−K _(rj) or e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)−K _(rj) wheree_(ij) is the intensity of a signal transmitted from an i^(th)transmitting station at (xi,yi) and received at a j^(th) receivingstation at (uj, vj), d_(ij) is the distance from the i^(th) transmittingstation to the j^(th) receiving station expressed as d _(ij)={squareroot}{square root over ((x _(i) −u _(j))²+(y _(i) −v _(j))²)}, S1 and S2are correcting coefficients, and K_(rj) is an environmental coefficientfor the receiving station, wherein the positioning computer determinesthe coefficients S1, S2 and K_(rj) using the known position informationto estimate the position of the unknown transmitting station.
 10. Thesystem according to claim 9, wherein when using e _(ij) =f ₀(d _(ij))=S₁×log₁₀(d _(ij))+S ₂ −K _(rj) as the first correcting formula, thepositioning computer derives a distance $\begin{matrix}{{md}_{ij} = 10^{{({e_{ij} - S_{2} + K_{rj}})}/S_{1}}} & (4)^{\prime\prime\prime}\end{matrix}$

from the measured intensity, and determines an estimation functionh_(ij) = ∑(10^((e_(ij) − S₂ + K_(rj))/S₁) − d_(ij))²,

and when using e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)−K _(rj) asthe first correcting formula, the positioning computer derives adistance md_(ij) = 10^((e_(ij) + K_(rj))/(S₁)) − S₂

from the measured intensity, and determines an estimation functionh_(ij) = ∑(10^((e_(ij) + K_(rj))/(S₁)) − S₂ − d_(ij))²

to weight with h_(ij)/md_(ij) to estimate the position of the unknowntransmitting station.
 11. The system according to claim 6 wherein thefirst correcting formula is e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂−K _(ti) or e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂)−K _(ti) wheree_(ij) is the intensity of a signal transmitted from an i^(th)transmitting station at (xi,yi) and received at a j^(th) receivingstation at (uj, vj), d_(ij) is the distance from the i^(th) transmittingstation to the j^(th) receiving station expressed as d _(ij)={squareroot}{square root over ((x _(i) −u _(j))²+(y _(i) −v _(j))²)}, S1 and S2are correcting coefficients, and K_(ti) is an environmental coefficientfor the transmitting station, wherein the positioning computerdetermines the coefficients S1, S2 and K_(ti) using the known positioninformation to estimate the position of the unknown transmittingstation.
 12. The system according to claim 11, wherein when using e_(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij))+S ₂ −K _(ti) as the firstcorrecting formula, the positioning computer derives a distancemd_(ij) = 10^((e_(ij) − S₂ + K_(ti))/S₁)

from the measured intensity, and determines an estimation functionh_(ij) = ∑(10^((e_(ij) − S₂ + K_(ti))/S₁) − d_(ij))²,

and when using e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)−K _(ti) asthe first correcting formula, the positioning computer derives adistance md_(ij) = 10^((e_(ij) + K_(ti))/(S₁)) − S₂

from the measured intensity, and determines an estimation functionh_(ij) = ∑(10^((e_(ij) + K_(ti))/(S₁)) − S₂ − d_(ij))²

to weight with h_(ij)/md_(ij) to estimate the position of the unknowntransmitting station.
 13. The system according to claim 1, wherein thereceiving station comprises: an activation signal generator configuredto generate an activation signal for causing the transmitting station totransmit a second ID signal containing a second identifier; atransmitter configured to transmit the activation signal to thetransmitting station; and a time computation unit configured to measurea transmission time required to acquire the second identifier from thetransmitting station in response to the activation signal.
 14. Thesystem according to claim 13, wherein the positioning computerdetermines a second correcting formula defining a relation between apropagation time of a signal through the air and a distance between thetransmitting station and the receiving station, and estimates a positionof an unknown transmitting station using the second correcting formulaand known position information.
 15. The system according to claim 14,wherein the second correcting formula is expressed as p _(ij) =f ₁(t_(ij) ,e _(ij))=t _(ij) −B−g exp(−h×e _(ij))=Kd _(ij) =K{squareroot}{square root over ((u _(i) −u _(j))²+(v _(i) −v _(j))²)} wherewhere e_(ij) is the intensity of the second ID signal transmitted froman i^(th) transmitting station at (xi,yi) and measured at a j^(th)receiving station at (uj, vj), t_(ij) is the transmission time, p_(ij)is the propagation time, d_(ij) is the distance from the i^(th)transmitting station to the j^(th) receiving station expressed as d_(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j))²)}, B, g, and h are correcting coefficients, and K is aproportional constant, and wherein the positioning computer determinesthe correcting coefficients B, g, and h, and the proportional constant Kfrom the known position information to estimate the position of theunknown transmitting station.
 16. The system according to claim 15,wherein the positioning computer derives a distancend_(i  j) = p_(i  j)/K = {t_(i  j) − B − g  exp (−h × e_(i  j)}/K

from the propagation time through the air, and determines an estimationfunctionhh_(i  j) = ∑({t_(i  j) − B − g  exp (−h × e_(i  j))}/K − d_(i  j))²

using the derived distance to weight with hh_(ij)/nd_(ij) to estimatethe position of the unknown transmitting station.
 17. The systemaccording to claim 1, wherein the receiving station includes afixed-position receiving station and a moving receiving station, andwherein the positioning computer carries out the steps of: (a)determining a first correcting formula defining a relation between theintensity of a received signal and a distance using known positioninformation supplied from the fixed-position receiving station; (b)estimating the position of the moving receiving station using the firstcorrecting formula, together with signal information transmitted from aknown or position-estimated transmitting station and positioninformation about said known or position-estimated transmitting station;and (c) estimating a position of an unknown transmitting station basedon signal information transmitted from said unknown transmitting stationto the fixed-position receiving station or the moving receiving stationat an estimated position, and position information about thefixed-position receiving station and said estimated position of themoving receiving station, and wherein the positioning computer repeatsthe steps (b) and (c) to successively estimate positions of multipleunknown transmitting stations as the moving receiving station travels.18. The system according to claim 13, wherein the receiving stationincludes a fixed-position receiving station and a moving receivingstation, and wherein the positioning computer carries out the steps of:(a) determining a second correcting formula defining a relation betweena signal propagation time through the air and a distance using thetransmission time and the intensity measured at the fixed-positionreceiving station and known position information supplied from thefixed-position receiving station; (b) estimating a current position ofthe moving receiving station using the second correcting formula,together with signal information transmitted from a known orposition-estimated transmitting station to the moving station, positioninformation about said known or position-estimated transmitting station,and a transmission time measured at the moving receiving station; and(c) estimating a position of an unknown transmitting station based onsignal information transmitted from said unknown transmitting station tothe fixed-position receiving station or the moving receiving station atan estimated position, position information about the fixed-positionreceiving station and said estimated position of the moving receivingstation, and a transmission time measured at the fixed-positionreceiving station or the moving receiving station at the estimatedposition, and wherein the positioning computer repeats the steps (b) and(c) to successively estimate positions of multiple unknown transmittingstations as the moving receiving station travels.
 19. The systemaccording to claim 1, wherein the receiving station includes a singlemoving receiving station, and wherein the positioning computer carriesout the steps of: (a) determining a first correcting formula defining arelation between the intensity of a received signal and a distance usingsignal information transmitted from a transmitting station whoseposition is known to the moving receiving station at an unknownposition, and position information of said transmitting station; (b)estimating a current position of the moving receiving station using thefirst correcting formula, based on signal information transmitted from aknown transmitting station or a position-estimated transmitting stationand position information about said known transmitting station or theposition-estimated transmitting station; and (c) estimating a positionof an unknown transmitting station based on signal informationtransmitted from said unknown transmitting station to the movingreceiving station at the estimated current position, and positioninformation about the estimated current position, and wherein thepositioning computer repeats the steps (b) and (c) to successivelyestimate positions of multiple unknown transmitting stations as themoving receiving station travels.
 20. The system according to claim 13,wherein the receiving station includes a single moving receivingstation, and wherein the positioning computer carries out the steps of:(a) determining a second correcting formula defining a relation betweena signal propagation time through the air and a distance using signalinformation transmitted from a transmitting station whose position isknown to the moving receiving station at an unknown position, positioninformation of said transmitting station, and the transmission timemeasured at the moving receiving station; (b) estimating a currentposition of the moving station using the second correcting formula,based on signal information transmitted from the known transmittingstation or a position-estimated transmitting station, positioninformation about said known transmitting station or theposition-estimated transmitting station, and the transmission timemeasured by the moving receiving station; and (c) estimating a positionof an unknown transmitting station based on signal informationtransmitted from said unknown transmitting station to the movingreceiving station at the estimated current position, positioninformation about the estimated current position, and the transmissiontime measured by the moving receiving station at the estimated currentposition, and wherein the positioning computer repeats the steps (b) and(c) to successively estimate positions of multiple unknown transmittingstations as the moving receiving station travels.
 21. The systemaccording to claim 1, wherein the first ID signal is transmitted usingelectromagnetic waves or sound waves.
 22. The system according to claim2, wherein the first and second ID signals are transmitted usingelectromagnetic waves or sound waves, and the activation signal istransmitted using electromagnetic waves or sound waves.
 23. The systemaccording to claim 6, wherein if the intensity of the first ID signaltransmitted form an i^(th) transmitting station is measured at a j^(th)receiving station, but is not measured at an m^(th) receiving station,then the positioning computer determines the first correcting formulaadding an restrictive condition d_(ij) <d _(im) where d_(ij) is adistance between the i^(th) transmitting station and the j^(th)receiving station, and d_(im) is a distance between the i^(th)transmitting station and the m^(th) receiving station.
 24. A method fordetermining a position of an object comprises the steps of: receiving ata receiving station a first ID signal containing a first identifiertransmitted from a transmitting station; measuring an intensity of thefirst ID signal received at the receiving station; determining a firstcorrecting formula defining a relation between the intensity of thereceived signal and a distance; and estimating a position of an unknowntransmitting station using the first correcting formula and knownposition information.
 25. The method according to claim 24, wherein thefirst correcting formula is expressed as e _(ij) =f ₀(d _(ij))=S₁×log₁₀(d _(ij))+S ₂ or e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d _(ij) +S ₂)where e_(ij) is the intensity of a signal transmitted from an i^(th)transmitting station at (xi,yi) and measured at a j^(th) receivingstation at (uj, vj), d_(ij) is the distance from the i^(th) transmittingstation to the j^(th) receiving station expressed as d _(ij)={squareroot}{square root over ((x _(i) −u _(j))²+(y _(i) −v _(j))²)}, and S1and S2 are correcting coefficients.
 26. The method according to claim25, further comprising the step of deriving a distancemd_(i  j) = 10^((e_(i  j) − S₂)/S₁)

from the measured intensity if using e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d_(ij))+S ₂ as the first correcting formula and determining an estimationfunction$h_{i\quad j} = {\sum\limits_{j = 1}^{rn}( {10^{{({e_{i\quad j} - S_{2}})}/S_{1}} - d_{i\quad j}} )^{2}}$

to weight with h_(ij)/md_(ij) to estimate the position of the unknowntransmitting station.
 27. The method according to claim 25, furthercomprising the step of deriving a distancemd_(i  j) = 10^((e_(i  j))/(S₁)) − S₂

from the measured intensity if using e _(ij) =f ₀(d _(ij))=S ₁×log₁₀(d_(ij) +S ₂) as the first correcting formula and determining anestimation functionh_(i  j) = ∑(10^((e_(i  j))/(S₁)) − S₂ − d_(i  j))²

to weight with h_(ij)/md_(ij) to estimate the position of the unknowntransmitting station.
 28. The method according to claim 24, furthercomprising the steps of: transmitting an activation signal from thereceiving station to the transmitting station; transmitting a second IDsignal containing a second identifier from the transmitting station tothe receiving station in response to the activation signal; measuring atransmission time required to acquire the second ID signal in responseto the activation signal at the receiving station; determining a secondcorrecting formula defining a relation between a signal propagation timethrough the air and a distance based on the measured transmission time;and estimating a position of an unknown transmitting station using thesecond correcting formula and known position information.
 29. The methodaccording to claim 28, wherein the second correcting formula is p _(ij)=f ₁(t _(ij) ,e _(ij))=t _(ij) −B−g exp(−h×e _(ij) )=Kd _(ij) =K{squareroot}{square root over ((u _(i) −u _(j))²+(v _(i) −v _(j))²)} wheree_(ij) is the intensity of the second ID signal transmitted from ani^(th) transmitting station at (xi,yi) and measured at a j^(th)receiving station at (uj, vj), t_(ij) is the transmission time, p_(ij)is the propagation time, d_(ij) is the distance from the i^(th)transmitting station to the j^(th) receiving station expressed as d_(ij)={square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v_(j))²)}, B, g, and h are correcting coefficients, and K is aproportional constant, and wherein the positioning computer determinesthe correcting coefficients B, g, and h, and the proportional constant Kfrom the known position information to estimate the position of theunknown transmitting station.
 30. A method for determining a position ofan object comprising the steps of: (a) determining a first approximatefunction e _(ij) =f ₀(d _(ij))=f ₀({square root}{square root over ((u_(i) −x _(j))²+(v _(i) −y _(i))²)}) as a first correcting formula, usinga first intensity e_(ij) of a first signal transmitted from at least oneknown transmitting station “i” located at a known position (ui, vi) andmeasured at a receiving station “j” located at a first unknown position(xj,yj), as well as a distance d_(ij) from the transmitting station “i”to the receiving station “j”, to derive a position (uj, vj) of the firstunknown position of the receiving station “j”; (b) defining a secondapproximate function e _(ij) =f ₀({square root}{square root over ((x_(i) −u _(j))²+(y _(i) −v _(j))²)}) based on the first correctingformula, using a second intensity e_(ij) of a second signal transmittedfrom an unknown transmitting station “i” located at an unknown position(xi, yi) and measured at a known or position-estimated receiving station“j”, as well as position information (uj, vj) of said known orposition-estimated receiving station “j”, to derive a position (ui, vi)of said unknown transmitting station “i”; and (c) defining a thirdapproximate function e _(ij) =f ₀({square root}{square root over ((u_(i) −x _(j))²+(v _(j) −y _(j))²)}) based on the first correctingformula, using a third intensity e_(ij) of a third signal transmittedfrom a known or position-estimated transmitting station “i” located at(ui,vi) and measured at the receiving station “j” at a second unknownposition, as well as position information of said known orposition-estimated transmitting station “i”, to derive a position (uj,vj) of the second unknown position of the receiving station “j”, thesteps (b) and (c) being repeated to successively estimate positions ofan unknown receiving station and an unknown transmitting station.
 31. Amethod for determining a position of an object comprising the steps of:(a) determining a first approximate function e _(ij) =f ₀(d _(ij))=f₀({square root}{square root over ((x _(i) −u _(j))²+(y _(i) −v _(j))²)})as a first correcting formula, using a first intensity e_(ij) of a firstsignal transmitted from a first unknown transmitting station “i” locatedat a first known position (xi,yi) and measured at one or more knownreceiving stations “j” located at known positions (uj,vj), as well as adistance d_(ij) from the transmitting station “i” to the receivingstation “j”, to derive a position (ui, vi) of the first unknowntransmitting station “i”; (b) defining a second approximate function e_(ij) =f ₀({square root}{square root over ((u _(i) −x _(j))²+(v _(i) −y_(j))²)}) based on the first correcting formula, using a secondintensity e_(ij) of a second signal transmitted from a known orposition-estimated transmitting station “i” located at (ui, vi) andmeasured at an unknown receiving station “j” located at an unknownposition (xj, yj), as well as position information (ui, vi) of saidknown or position-estimated transmitting station “i”, to derive aposition (uj, vj) of said unknown receiving station “j”; and (c)defining a third approximate function e _(ij) =f ₀({square root}{squareroot over ((x _(i) −u _(j))²+(y _(i) −v _(j))²)} based on the firstcorrecting formula, using a third intensity e_(ij) of a third signaltransmitted from a second unknown transmitting station “i” located at asecond unknown position (xi,yi) and measured at a known orposition-estimated receiving station “j” at (uj, vj), as well asposition information of said known or position-estimated receivingstation “j”, to derive a position (ui, vi) of the second unknownposition of the second unknown transmitting station “i”, the steps (b)and (c) being repeated to successively estimate positions of an unknowntransmitting station and an unknown receiving station.
 32. A method fordetermining a position of an object comprising the steps of: (a)determining a first approximate function p _(ij) =f ₁(t _(ij) ,e_(ij))=Kd _(ij) =K{square root}{square root over ((u _(i) −x _(j))²+(v_(i) −y _(j))²)} and a constant K as a second correcting formula, usinga first intensity e_(ij) of a first signal transmitted from at least oneknown transmitting station “i” located at a known position (ui,vi) andmeasured at a receiving station “j” located at a first unknown position(xj,yj), as well as a first signal transmission time tij, a first signalpropagation time pij through the air, and position information of saidknown transmitting station, to derive a position (uj, vj) of the firstunknown position of the receiving station “j”; (b) defining a secondapproximate function f ₁(t _(ij) ,e _(ij))=K{square root}{square rootover ((x _(i) −u _(j))²+(y _(i) −v _(j))²)} based on the secondcorrecting formula, using a second intensity e_(ij) of a second signaltransmitted from an unknown transmitting station “i” located at anunknown position (xi, yi) and measured at a known or position-estimatedreceiving station “j”, as well as a second signal transmission time(tij) and position information (uj, vj) of said known orposition-estimated receiving station “j”, to derive a position (ui, vi)of said unknown transmitting station “i”; and (c) defining a thirdapproximate function f ₁(t _(ij) ,e _(ij))=K{square root}{square rootover ((u _(i) −x _(j))²+(v _(i) −y _(j))²)} based on the secondcorrecting formula, using a third intensity e_(ij) of a third signaltransmitted from a known or position-estimated transmitting station “i”located at (ui,vi) and measured at the receiving station “j” at a secondunknown position, as well as a third signal transmission time (tij) andposition information of said known or position-estimated transmittingstation “i”, to derive a position (uj, vj) of the second unknownposition of the receiving station “j”, the steps (b) and (c) beingrepeated to successively estimate positions of an unknown receivingstation and an unknown transmitting station.
 33. A method fordetermining a position of an object comprising the steps of: (a)determining a first approximate function p _(ij) =f ₁(t _(ij) ,e_(ij))=Kd _(ij) =K{square root}{square root over ((x _(i) −u _(j))²+(y_(i) −v _(j))²)} as a second correcting formula, using a first intensitye_(ij) of a first signal transmitted from a first unknown transmittingstation “i” located at a first known position (xi,yi) and measured atone or more known receiving stations “j” located at known positions(uj,vj), as well as a first signal transmission time (tij), a firstsignal propagation time (pij) through the air, and position informationof said known receiving station “j”, to derive a position (ui, vi) ofthe first unknown transmitting station “i”; (b) defining a secondapproximate function f ₁(t _(ij) ,e _(ij))=K{square root}{square rootover ((u _(i) −x _(j))²+(v _(i) −y _(j))²)} based on the secondcorrecting formula, using a second intensity e_(ij) of a second signaltransmitted from a known or position-estimated transmitting station “i”located at (ui, vi) and measured at an unknown receiving station “j”located at an unknown position (xj, yj), as well as a second signaltransmission time (tij) and position information (ui, vi) of said knownor position-estimated transmitting station “i”, to derive a position(uj, vj) of said unknown receiving station “j”; and (c) defining a thirdapproximate function f ₁(t _(ij) ,e _(ij))=K{square root}{square rootover ((x _(i) −u _(j))²+(y _(i) −v _(j))²)} based on the secondcorrecting formula, using a third intensity e_(ij) of a third signaltransmitted from a second unknown transmitting station “i” located at asecond unknown position (xi,yi) and measured at a known orposition-estimated receiving station “j” at (uj, vj), as well as a thirdsignal transmission time (tij) and position information of said known orposition-estimated receiving station “j”, to derive a position (ui, vi)of the second unknown position of the second unknown transmittingstation “i”, the steps (b) and (c) being repeated to successivelyestimate positions of an unknown transmitting station and an unknownreceiving station.